Bill Belichick -- I Didn't Deflate the Footballs ... 'No Explanation for What Happened'

New England Patriots head coach Bill Belichick says he "had no knowledge" of the deflate-gate scandal until Monday morning ... and has "no explanation" for why the team's balls were under-inflated.

Belichick says the team has complied with the NFL investigation into the AFC Championship game -- in which the Pats were using under-inflated balls, which some say are easier to throw and catch.

Bill told the media, "I have no explanation for what happened."

Belichick explained that giving his team an advantage by tampering with the footballs has "never been a priority for me."

In fact, Bill says ... for years he has made his team practice with crappy footballs -- "the balls we practice with are as bad as they can be" -- and has never even thought about deflating the footballs to make it easier for his team.

"I've told you all I know about the subject from my perspective ... I don't have an explanation."