Speaking to reporters (via ESPN.com's Jeremy Fowler), Roethlisberger called Brown "the best in the world" and noted the team is frustrated by its 0-1-1 start.
"When you're the best in the world, you want to help participate, you want to win football games. We're all a little frustrated that we're not winning right now. ... AB is a very passionate football player, I think we all know that, the fans know that. That's what makes him special, the passion he has for this game and the passion to be great. We're not going to want to take that away from him."
It's been a turbulent period for the Steelers following their 42-37 loss to the Kansas City Chiefs in Week 2.
Former Steelers employee Ryan Scarpino tweeted Sunday that Brown "needs to thank his lucky stars" he was drafted by a team that had Roethlisberger at quarterback, and Roethlisberger is the reason Brown has produced at a high level in the NFL.
Brown responded to Scarpino: "Trade me let's find out."
After Brown missed practice on Monday, his agent, Drew Rosenhaus, issued a statement on behalf of his client (h/t ESPN's Adam Schefter):
"The tweet yesterday was not in reference to anything other than Antonio responding to a person he knows. It was not directed towards a trade or wanting to be [traded]. Any idea he was asking for a trade is not accurate.
"Antonio had a personal matter. I talked to the team about it. His issue was unrelated to the tweet or his relationship with the team. Third, AB has an incredible drive to win. He just wants to win. That's all that that is.
"That's not anything more than him encouraging his coaches and teammates to win. And that's what his entire focus is on. Any notion, any speculation otherwise, can be put to bed. This is a non-story that has been blown out of proportion. We can end this right here and now."
Brown leads the NFL with 33 targets and is tied for fourth with 18 receptions. His 8.9 yards per reception is well below his career average of 13.4 and he has just one catch of at least 20 yards through two games.
The Steelers will go for their first win of the season when they play the Tampa Bay Buccaneers on Monday Night Football.