The five-time Super Bowl champion, who is on friendly terms with Trump, told Boston's WEEI sports radio he was unhappy with the president's comments.
"Yeah, I certainly disagree with what he said," Brady said. "I thought it was just divisive. I just want to support my teammates. I am never one to say, 'Oh, that is wrong. That is right.'
"I do believe in what I believe in. I believe in bringing people together and respect and love and trust. Those are the values that my parents instilled in me and that's how I try to live every day."
Brady was speaking a day after around 16 Patriots players kneeled during the national anthem as a wave of protests erupted across the NFL.
Brady stood for the anthem but linked arms with team-mates before leading the Patriots to a 36-33 win over the Houston Texans at Gillette Stadium.
Trump had angered NFL players, owners and league officials after a tirade on Friday in which he described athletes protesting The Star-Spangled Banner to draw attention to racial injustice as "sons of bitches" who should be fired.
Brady meanwhile said he had heard Patriots fans who booed the team's protest, but said he had no issue with supporters who had shouted at kneeling player to stand up.
"I think everyone has a right to do whatever they want to do," Brady said when asked if he was dismayed by the fans.
"If you don't agree with it, that's fine, you can voice your disagreement; I think that's great. It's part of our democracy, as long as it's done in a peaceful, respectful way. That's what this country has been all about."