"At no time did any of our players ever cross the white line to intentionally hurt another player," Vitt told reporters Tuesday during a pre-draft news conference.
Vitt, who has been suspended six games for his role in the program, added that he was passionate about "player safety and making this a better league for player safety. ... I'm serving a six-game suspension for the spoken word, not the clenched fist. I am on board with (NFL Commissioner Roger Goodell)."
The league could hand down punishment this week to a number of Saints defenders for their roles in the program, which financially rewarded defensive players for knockout and cart-off hits, among other things.
Coach Sean Payton received a season-long suspension without pay, and general manager Mickey Loomis was banned eight games for their roles in the program. The NFL suspended former Saints defensive coordinator Gregg Williams indefinitely for the program, and the team was fined $500,000 and docked second-round draft picks this year and in 2013..
Vitt, who will fill in for Payton this season, said it has been difficult without his boss.
"I have not talked to Sean in a week and a half. ... It's the longest I've gone not talking to Sean in 10 years," Vitt said. "Sean's my friend. Sean's our leader here, and I can't take Sean Payton's place ... There's not a player, administrator or anybody in this building that doesn't talk about Sean and ask about Sean on a daily basis.
"We've got to move forward. It is what it is right now, and there's nothing we can do about it."
Vitt also called Monday's allegations that Loomis had the ability to eavesdrop on opposing coaches' radio chatter during games, "absolutely ludicrous."
"That's something from 'Star Wars,' " he said. "It's irresponsible. Mickey Loomis has amazing credibility."
Loomis, who's under investigation by federal and state authorities, has denied the allegations from an unnamed source.