Ovechkin told ESPN.com on Friday that he thought it was classless of Bradley to speak ill of his former mates.
"Well, I think if you leave a team, you can't say bad things about the players and the team," Ovechkin said. "I think it looks stupid, especially when you say that to media. If you want to say something to the face, you have to say it to the face, but why have to say it to the media?
"Like Brads left, I'm not going to say bad things about him."
Bradley, now on the Florida Panthers' roster, also questioned the coaching philosophy of coach Bruce Boudreau and said the Capitals were too nonchalant in the playoffs.
Ovechkin said if players have issues with each other, they should be dealt with in the locker room, not in the media.
"Why you have to do this? I don't respect that," Ovechkin said. "I think it was bad. I think the players know that. It has to be in the locker room, and nothing has to go out from the locker room. We're all players. We all respect each other, but I don't want to say bad things about Brads or different guys that left.
"I think it's stupid."
Ovechkin registered 85 points last season, good for seventh in the league in scoring, but it was a significant drop-off for the former scoring champion, who compiled 109, 110 and 112 points in his three previous seasons.
He admitted he needs to be better this season.
"My personal game, of course, I want to get better than I was last year," Ovechkin said. "I don't think it matters what we change in systems or what, I still have a chance to score goals, I still have a chance to make some great plays, but I didn't and that's how I want to get better this year."
The rambunctious winger added that he needs to be less passive in his game and be better at puck pursuit.
"I think about it all the time, what I have to do better. I'm still learning. I'm only 25," he said.
In spite of his criticisms of the Capitals, Bradley praised Ovechkin, saying he was an "all-in kind of guy." However, Bradley did note that Ovechkin needs to take better care of himself.
"I never worry about Ovi," Bradley said.
"Ovi has some growing up to do as far as taking care of himself and things like that, but as far as his want to win, he really does just want to win the games."
As for Ovechkin's own take on his leadership, he was emphatic that there is not too much pressure on him as captain.
"I'm the captain of this team and this is my team and I'm going to do my best," he said.
"If team trusts me, my coach trusts me, I'm going to do my best."
Washington general manager George McPhee made some significant changes to the roster this offseason, adding Troy Brouwer, who won a Stanley Cup in Chicago in 2010; playoff star Joel Ward, who helped Nashville to its first playoff series win this past spring; and veteran center Jeff Halpern.
Ovechkin is bullish on the changes.
"Of course we make some changes," he said. "Sometimes it's hard to lose guys who you know, but it's nice to get some change and the team's getting better, we're all getting better with these changes."
The Capitals have all the ingredients to be a good team, Ovechkin said, but he knows only too well that means little, given the team's lackluster playoff success in recent years.
"Well, it's every time we say, 'This is the year for the Caps,' but let's wait and we're going to see," he said.