"To suggest that I destroyed a phone to avoid giving the NFL information it requested is completely wrong," he said in a verified Facebook posting.
Also on Wednesday, team owner Robert Kraft said he fully supported Brady and regretted cooperating with the NFL in the investigation.
"I was wrong to put my faith in the league," he said at a news conference at the team's training camp.
The Deflategate controversy erupted after the Patriots won January's AFC championship game over the Indianapolis Colts. The thrust of the accusations is that the team knowingly used under-inflated footballs for a competitive advantage. Brady, who led the team to a Super Bowl victory, has denied involvement over and over.
NFL Commissioner Roger Goodell on Tuesday affirmed the suspension
of Brady he handed down in May, saying new information showed Brady tried to hide evidence by breaking his cell phone.
The NFL had asked to see the phone's text messages but lacked subpoena power to force Brady to comply. Now, the text messages are gone and cannot be retrieved, according to a letter from the football star's cell phone provider.
Brady: 'I did nothing wrong'
In the Wednesday Facebook posting, Brady said that "I did nothing wrong, and no one in the Patriots organization did either." He added that he replaced his broken Samsung phone with a new iPhone 6 after his attorneys told the NFL "my actual phone device" would not be investigated. His representatives turned over requested cell phone records and emails, Brady said, and tried to obtain text messages from his old phone.
The phone company information showed who received and sent text messages, but not what the texts said.
Brady said that as a union member, he didn't want to set a precedent by handing over his phone. He said investigators never told him that failing to provide the phone would result in any discipline.
"Most importantly, I have never written, texted, emailed to anybody at anytime, anything related to football air pressure before this issue was raised at the AFC Championship game in January," he said. "There is no 'smoking gun' and this controversy is manufactured to distract from the fact they have zero evidence of wrongdoing."
Kraft: 'This was never about doing what was fair and just'
At his news conference, Kraft said he "unequivocally" supports Brady, apologized to Brady and the team's fans, and insisted the league "still has no hard evidence of anybody doing anything" to tamper with football inflation levels.
Kraft said he accepted the league's penalty against the Patriots -- a $1 million fine and forfeiture of draft picks the next two years -- because he thought cooperating would help exonerate Brady. The league ended up suspended Brady for four games.
"I have come to the conclusion that this was never about doing what was fair and just," Kraft said.
The NFL Players Association filed an appeal Wednesday on Brady's behalf, asking a federal court in Minnesota to overturn the four-game suspension, the players' union announced on its website.
The move follows by a day an NFL's maneuver. It filed a complaint Tuesday against the NFLPA in federal court in New York, asking a judge to confirm the decision to uphold Brady's suspension.
The union said a Minnesota court has jurisdiction because one of the 32 NFL teams -- the Vikings -- is headquartered in that district and the league regularly does business there.
Saga of a cell phone
The investigators, according to Goodell's final decision, had asked Brady's attorneys for the cell phone several times, on and before February 28. The NFL said it learned Brady told his assistant to break the phone March 6, a day Brady was interviewed by investigators.
It wasn't until June 18, almost four months after investigators had requested its data from Brady and five days before an appeals hearing, that Brady's lawyers informed the league the phone had been broken.
During the 10-hour-long appeals hearing at NFL headquarters in New York, Brady said the phone had been destroyed because it was his usual practice when he got a new mobile phone.
"We presented the commissioner with an unprecedented amount of electronic data, all of which is incontrovertible," said Don Yee, Brady's lawyer. "I do not think that any private citizen would have agreed to provide anyone with the amount of information that Tom was willing to reveal to the commissioner."
He said Goodell ignored electronic information, and "we don't know why."
The quarterback began using a new phone on March 6, leading the NFL to believe the previous one had been destroyed that day.
Reacting to the decision to uphold the suspension, the NFL players' union said on its website
: "The fact that the NFL would resort to basing a suspension on a smoke screen of irrelevant text messages instead of admitting that they have all of the phone records they asked for is a new low, even for them, but it does nothing to correct their errors."
Punishment for Patriots
Lawyer Ted Wells, who led the investigation, said Brady probably had at least a general knowledge about how the balls were deflated.
Brady said Wednesday: "It is disappointing that the commissioner upheld my suspension based upon a standard that it was 'probable' that I was 'generally aware' of misconduct. The fact is that neither I, nor any equipment person, did anything of which we have been accused."
The investigators' report said the likely perpetrators were equipment assistant John Jastremski and the man who carried the balls from the officials' locker room to the field, Jim McNally. The Patriots have suspended both employees indefinitely.