The permanent Red Devils manager transformed the club’s fortunes after taking charge in January, guiding them to a third-place finish.
Speaking to talkSPORT, Rooney praised the positive atmosphere around Old Trafford but warned supporters against expecting an immediate title challenge in Carrick’s first full season in charge.
"I think where Man United have been over the last few years has been very difficult for the fans to find some happiness in it," Rooney said.
"But I think since Michael went in, I think there’s hope and belief again within the Man United fans. To finish third, I think all of the signings done quite well.
“And now back in the Champions League, and hopefully they go and sign a few players who can help them try and go the next step."