Kompany was dismissed in the 12th minute for a sliding tackle on Nani, though the Belgian defender did appear to win the ball.
Rooney, who scored twice in the clash, ran to Foy after the challenge and appeared to appeal for action to be taken.
"It was not a red card. Rooney told him his decision. This type of tackle happened with Rio Ferdinand and other United defenders many times," Mancini said.
"The red card for Vinnie? No, it's impossible. But I don't want to talk about the referee because I want to stay on the bench for the next game."
City have confirmed that they will appeal Foy's decision, which carries a four-match ban for Kompany as he has already received a red card this season.