"No, certainly not," Brady said on the Boston radio station's "The Dennis & Callahan Show." "I don't know why these things come about, but they do. I think it's just a competitive media culture out there now.
"I love (Moss) as a person and a player. I don't think I ever had an altercation with a teammate. You demand a certain level of respect in the locker room, that's the culture of our team. I don't think I've seen any players in our locker room fight, that's just not the way it is."
In a pregame show Sunday, CBS analyst Charley Casserly reported that Brady and Moss "went toe-to-toe and had to be separated" the week before the trade.
Casserly, general manager of the Washington Redskins from 1989 to 1999 and Houston Texans from 2000 to 2006, said: "One of Brady's problems with Moss was his behavior as a Patriot. Then one of the things that was overheard was Brady telling Moss, 'You need to cut your beard.' Moss counters, 'You need to get your hair cut. You look like a girl.'"
"That's news to me," Belichick said Monday during a conference call.
Moss and Brady praised each other after the trade, as had been their custom in public comments throughout their three-plus seasons as teammates.
Brady refused to tell WEEI what the texts included, but Moss had a message for the quarterback following the Vikings' 29-20 loss.
"Tom, I know you watching buddy, I appreciate that text," Moss told reporters. "Sorry we didn't bring it home, buddy, but I appreciate the text."
Brady was asked if he had any say in the Moss trade.
"Certainly not. I'm a player on this team just like all the other players," he said. "Obviously, I talk a lot to the coaches and they talk to the players. They never come and say, 'Well, what do you think about this?' No. We show up to work and we do our job. And I think that's the best way to handle things as a player.
"I've become very emotional in the past about losing certain players, and I think that's affected me, which in turn has impacted the team," Brady added. "I think when you're an older player on the team and you've seen guys come and go, and you win and you lose, to be level-headed and to not be unemotional but to be maybe not surprised, you just go about your business and you try to put it behind you and move forward with the guys you've got, because that's what you really owe the team."
"Well, I have no idea," Brady said. "... With all due respect, with all the different questions I'm sure you guys have about Randy, he's moved on. He played for another team last night. And we've moved on. We had two practices last week and we're prepared to move on as we always have. And that doesn't diminish anything that he's done or has accomplished for our team, because he's obviously an exceptional player. But we've got a season to play."
"I don't think there's any one solution," Brady said. "You just don't replace a guy with Randy's talent and ability down the field. You replace it with maybe using the strengths of other players ... Randy certainly has his strengths. Wes (Welker) has his strengths. The tight ends have their strengths. I think it's up to the coaching staff when you game plan to determine what your players do the best, and those are the things that you ultimately do.
"I still think we have a lot of confidence that we can move the football," Brady added. "I think we still have some explosive players in the passing game, I don't think there's any doubt about that."
The Associated Press contributed to this report.