"I guess I am late," said Williams, who signed a six-year, $100 million contract with the Bills before last season.
Williams finished his injury-marred 2012 season with 10.5 sacks and was held without a sack in a season-opening loss to the New England Patriots.
"I don't think I've felt this way in the last five years," Williams said. "I finally feel like I am at peace, just as a person."
Williams called himself "one of the calmest persons you'll ever meet" but acknowledged his transition to Buffalo hasn't been as smooth as it could be.
"Just everything," Williams said when asked why he hadn't been "at peace" earlier. "Football is football, but you have a personal life and just life in general," Williams said. My mind-frame and my demeanor is just totally different."
The Bills were able to keep consistent pressure on Panthers quarterback Cam Newton throughout their comeback win. Defensive lineman Marcell Dareus had a half-sack, while linebacker Kiko Alonso closed out the game with Buffalo's sixth sack.