The ex-United midfielder has taken charge to the end of the season.
"It is probably the obvious choice really because I don't think there are any top, top managers available at the minute," Rooney said on the latest edition of BBC podcast The Wayne Rooney Show.
"I think it is the right choice at this moment in time.
"It is a difficult task of course. Where Manchester United are at the minute is not a good place and Michael has to go in and steady the ship."
Carrick's first game in charge will be against Manchester City on Saturday at Old Trafford.
"It is a massive game for the club, for Michael," Rooney said.
"I think what he will do is bring a bit of calmness, a bit of grit to the game, which I think is needed. It is going to be very difficult, Manchester City are obviously a top team and it will be difficult to get anything out of it even at Old Trafford.
"But as we've seen over the years, Manchester United if they do turn up can win the game and hopefully that happens on Saturday."