For more than a decade, Tom Brady has established himself as one of the greatest quarterbacks of all time, one of the sport’s most popular and respected players. On Wednesday, Brady may have jeopardized his credibility for good.

Like Patriots coach Bill Belichick, Brady denied having anything to do with footballs being deflated in the AFC Championship Game and denied knowing it had occurred until the next day, but to the quarterback’s former peers, the NFL’s golden boy lost some of the luster he had earned in his 15-year career.

“I did not believe what Tom had to say,” former quarterback and ESPN analyst Mark Brunell said. “Those balls were deflated. Someone had to do it and I don’t believe there’s an equipment manager in the NFL that would on his own initiative deflate a ball without the starting quarterback’s approval. I just didn’t believe what Tom Brady had to say.”

Former Steelers running back Jerome Bettis added, “I’m so disappointed because I thought this was a perfect opportunity for Tom Brady to go and say, ‘You know what? I made a mistake. I blew it. It’s on me. I’ll take the blame here, and this will go away.’ He didn’t do that … I’m disappointed in you, Tom Brady.”

Fellow ESPN analyst Brian Dawkins said it was “unbelievable” for Brady not to be aware when he touched the balls every play, while Hall of Famer Troy Aikman agreed that the balls would not be altered unless Brady had instructed an equipment manager to do so.

“It’s obvious that Tom Brady had something to do with this,” Aikman told a Dallas radio station — before either of Brady’s or Belichick’s denials. “For the balls to be deflated, that doesn’t happen unless the quarterback wants that to happen, I can assure you of that. Now the question becomes: Did Bill Belichick know about it?”

Incredibly, the already tarnished Belichick left his press conference earlier in the day with more plausible deniability, particularly to quarterbacks familiar with the ball-picking process.

“I listened to Bill Belichick and I believed every word he said,” eight-year NFL pro Matt Leinart told The Post. “Not once did a head coach ever have any input in that. It’s strictly a quarterback-to-equipment-manager thing and that’s pretty universal. Those are the only two guys that have any part of that process.

“You go through the whole bag and you literally handpick them and say, ‘This one is good, this one’s too hard, put a little bit of air in that one, take a little bit out. … It’s a full 20-minute process to make sure on Sunday you have the exact football you want to be throwing. Quarterbacks are very, very picky about how they want their ball and that goes on everywhere.”

Leinart, now an analyst with Fox Sports, said he saw numerous things done to balls in his career, including being rubbed with varying substances and thrown in dryers, to get the right feel. He said he didn’t consider it cheating because “every team doctors up the ball to the liking of their quarterback” and that while deflation would help Brady with his grip, it would take away velocity and distance on throws.

Nevertheless, Ravens defensive end Chris Canty — whose team lost to the Patriots in the AFC divisional round — thinks it is just another example of New England’s willingness to do anything to gain an unfair edge.

“The Patriots are habitual line-steppers,” Canty said while appearing on NBCSN on Wednesday. “If the allegations are true, then you are talking about attacking the integrity of our game and I have an issue with that.

“What I’m going to say about the deflating of the balls, to me there is no difference than performance-enhancing drugs. You are cheating at that point. You are getting a competitive advantage outside of the rule book and there has to be some sort of consequences for that.”

Aikman thinks the consequences should be harsher than the suspensions handed to the Saints for Bountygate in 2012, when NFL Commissioner Roger Goodell claimed ignorance was not an excuse.

“Sean Payton did not cheat,” Aikman said of the Saints coach who was suspended an entire year. “There was nothing that Sean Payton and the Saints did that was illegal. And they did not give themselves a competitive edge.

“Now twice, under Bill Belichick and possibly a third time, they’ve cheated and given themselves an advantage. To me, the punishment for the Patriots and/or Bill Belichick has to be more severe than what the punishment was for the New Orleans Saints.”

After a season filled with scandals — including Goodell’s indefensible decision to initially suspend Ray Rice two games in the former Ravens running back’s domestic violence case — Aikman thinks enormous pressure is on Goodell, especially due to his friendship with Patriots owner Robert Kraft.

“There’s a lot of coaches and a lot of people that look upon the Patriots as a team that’s been favored in some of the things that have happened — I thought the punishment he got for Spygate was a slap on the wrist, was next to nothing — so we’ll see,” Aikman said.