Former Penn State assistant football coach Jerry Sandusky insisted in an interview Monday night he is “innocent” of charges that he sexually abused young boys, denying to NBC’s Bob Costas that he’s a pedophile.

In a telephone interview with NBC’s “Rock Center With Brian Williams,” Sandusky admitted that some details in the graphic 23-page grand jury report released earlier this month are correct.

“I could say I have done some of those things,” he said. “I have horsed around with kids I have showered [with] after workouts. I have hugged them, and I have touched their legs without intent of sexual contact.”

Still, Sandusky claimed he has been falsely accused of crimes. When pressed, the 67-year-old Sandusky said the only thing he did wrong was having “showered with those kids.”

The stunning allegations led to the firing of legendary coach Joe Paterno and the departure of other officials because they didn’t promptly contact police after accusations surfaced. Investigations have been launched by the Pennsylvania attorney general’s office, the U.S. Department of Education, Penn State and Second Mile, the charity founded by Sandusky.

Costas asked directly: “Are you sexually attracted to underage boys?”

Sandusky repeated the question, paused, and responded, “No. I enjoy young people.”

Asked if Paterno had ever spoken to him about his behavior or expressed disapproval, Sandusky said simply, “No.”

And asked if he felt guilty over the spreading fallout that has affected the university and prominent university figures including the fired Paterno, Sandusky responded, “I don’t think it was my fault. I obviously played a part in this … I shouldn’t have showered with those kids. That’s what hits me the most.”

Sandusky’s lawyer, Joe Amendola, said Monday night that showering with children does not equate automatically to sexual assault.

“Jerry Sandusky is a big, overgrown kid. He’s a jock,” Amendola told CNN’s Jason Carroll. “The bottom line is jocks do that — they kid around, they horse around.”

But CNN legal analyst Sunny Hostin said she thinks a crime has already been committed, based on Sandusky’s own admissions.

“It’s such a classic fact pattern for him to admit that he showered with these children and horsed around and confessed to touching them,” she said on CNN’s “AC360.” “In my mind, that’s already misdemeanor child sex abuse. So I disagree when the attorney says nothing criminal happened here. That, in and of itself, is criminal … I’m flabbergasted.”

CNN senior legal analyst Jeffrey Toobin said Amendola finds himself in a difficult position in trying to explain his client’s actions.

“It is better to say they took a shower together than to say that sex took place in the shower. But when you are admitting to showering with a 10 year old, you got a big problem already.”

Veteran defense attorney Mark Geragos, who defended Michael Jackson against child molestation charges, urged caution in the case.

“Is there anyone who gives a presumption of innocence at this point? No,” Geragos said. “Before we go and we say this is a done deal … and condemn them and everything else, I think maybe we step back and take a deep breath for a second.”

Sandusky was arrested on November 5, after the release of the grand jury report detailing alleged crimes that he committed between 1994 and 2009. The grand jury identified eight young men allegedly targeted by Sandusky.

After his arrest, authorities have received more than a dozen calls from alleged victims of the former coach, a source close to the investigation told CNN last week. The source said it would take time to vet the allegations.

One incident witnessed by then-graduate assistant coach Mike McQueary in 2002 allegedly happened on Penn State’s campus.

McQueary told Paterno what he had seen, and Paterno then alerted then-athletic director Tim Curley, but law enforcement didn’t learn of the alleged incident until years later.

In the interview with NBC’s Costas, Sandusky flatly denied that McQueary witnessed what has been described in some accounts as Sandusky’s rape of a young boy. He said instead that he and the boy were in the shower, “snapping towels” and engaging in horseplay.

Regarding the 2002 incident, Amendola said “the kid was messing around and having a good time” in the shower with Sandusky, adding that McQueary felt “uncomfortable” upon seeing it. He denied the more graphic details offered in that and other allegations, claiming that the prosecution’s case lacked sufficient evidence and witnesses.

“We believe we’ve found him and if we have found him, he’s telling a very different story than Mike McQueary and that’s big news,” Amendola told NBC’s Today show. He said the person in question claims the alleged rape never happened.

Amendola said that Victim 4 named in the grand jury presentment was at Sandusky’s house as recently as two years ago. He was there with his girlfriend and baby and said he wanted Sandusky and his wife “to be part of his family.” He said two others mentioned in the presentment saw Sandusky this summer and went to dinner with him.

“They have been throwing everything they can throw up against the wall,” Amendola said of prosecutors’ case. ” And they’re saying, [out of] all these accusations, some of them have to be true. But when you take it apart, they don’t even have victims in several of their cases.”

After Sandusky was charged this month with 40 counts of sexually abusing children, Judge Leslie Dutchcot freed him on $100,000 bail, against the wishes of prosecutors.

A biography of Dutchcot posted on the website of the law firm Goodall & Yurchak lists her as a volunteer for Second Mile, the charity Sandusky founded. It is not clear whether Dutchcot currently has any affiliation with the organization.

CNN tried to contact the judge but has not received a response.

School trustees fired university President Graham Spanier and Paterno last week on the heels of Sandusky’s arrest, while McQueary was put on administrative leave.

And on Monday, in an indication of the scandal’s fallout spreading beyond Penn State, U.S. Navy spokeswoman Lt. Cmdr. Alana Garas said that the U.S. Navy secretary recommended that Spanier “be removed from the board of advisers to the presidents of the Naval Postgraduate School and Naval War College.”

Also on Monday, the board of directors for the charity that Sandusky founded – Second Mile – announced that its CEO had resigned. The CEO of 28 years, Jack Raykovitz, a licensed psychologist, “and the board believe this is in the best interests of the organization,” said a statement.

David Woodle, the board’s vice chairman, will take over day-to-day operations.

Saying that the “safety and well-being of the children” is central to its mission, the board announced it will conduct an internal investigation and make “recommendations regarding the organization’s future operations. We hope to have those findings by the end of December.”

Second Mile vowed to cooperate fully with the ongoing state attorney general’s investigation. It will conduct an internal investigation and has retained the Archer & Greiner law firm, which includes former Philadelphia district attorney Lynne Abraham.

Penn State announced a probe last week and the U.S. Department of Education wants to know whether Penn State failed to comply with the Clery Act, which requires colleges and universities “to disclose the number of criminal offenses on campus that are reported each year.”

The Office of Federal Student Aid is conducting the probe.

“In addition, in certain cases, the institution must issue a timely warning if a reported crime represents a threat to the campus community,” the department said.

Sandusky molested young boys after developing close relationships with them through Second Mile, according to the grand jury report.

The group said Sandusky has not been involved with its children since he told officials in November 2008 he was being investigated over “allegations made against him by an adolescent male.”

Sandusky and his wife were a host family through another charity, the New York-based Fresh Air Fund, which sends inner-city children to volunteer families and camps in non-urban locales, spokeswoman Andrea Kotuk said. She added that the charity isn’t yet sure when the Sanduskys were hosts, saying workers there were reviewing records and cooperating with authorities in Pennsylvania.

On November 7 – two days after Sandusky’s arrest – the ex-wife of Sandusky’s adopted son filed a petition for “temporary emergency modification of custody,” according to a filing by the woman’s lawyer Justine F. Andronici.

Jill Jones asked that her ex-husband, Matt Sandusky, “not permit the children to be around Jerry Sandusky and that the children not be taken to Dorothy and Jerry Sandusky’s residence.” The document claims that Matt Sandusky took the children to his parents’ home on the day before the request was filed.

The Sanduskys’ neighborhood has been affected as well, with the road to his home blocked off and private property signs up on his lawn after police said a cinder block was thrown through a window there.

Curley and Senior Vice President for Finance and Business Gary Schultz have been charged with failing to report the abuse to authorities and misleading investigators. Prosecutors determined they had a legal duty to report the alleged abuse, but not McQueary and Paterno.

On Monday, the Big Ten Conference announced that Paterno’s name is being pulled from the football championship trophy to be awarded next month at the conference’s first championship game in Indianapolis, Indiana.

“The trophy and its namesake are intended to be celebratory and aspirational, not controversial,” Big Ten Commissioner Jim Delany said in a statement. “We believe that it’s important to keep the focus on the players and the teams that will be competing in the inaugural championship game.”

The trophy was going to be named after both Paterno, the winningest coach in top-level college football history, and Amos Alonzo Stagg, a founder of the Big Ten. It will now be called the Stagg Championship Trophy.

New Penn State President Rodney Erickson, meanwhile, tried to help his school move on Monday — after a week that he said “tested the character and resilience of the Penn State community.”

In a statement on the school’s website, Erickson said he wanted to say “how proud of I am” of the school. He cited a candlelight vigil for abuse victims that thousands took part in Friday night and the Penn State-Nebraska football game on Saturday, which included a moment of silence.

“Today, we are back to class and the business of running this university,” he wrote.

“Collectively, we need to show the nation and world that Penn State cares, and that Penn State is a community of individuals committed to moving forward with a shared sense of purpose.”

CNN’s Mary Snow and Sarah Hoye reported from State College; Josh Levs, Monte Plott, Dana Ford and Joe Sterling from Atlanta; and Barbara Starr from Washington.