Kompany, who will now serve a four-game ban if City fail in their intended appeal, won the ball but was shown a straight red card by referee Chris Foy for lunging in two-footed at Nani.
Mancini, who was criticised for waving an imaginary card after an incident in last Tuesday's game against Liverpool, was disappointed with United striker Rooney's actions after the tackle.
The Italian said: "It was not a red card. Rooney told him his decision."
When asked to clarify whether he felt Rooney had influenced the decision, Mancini said: "Yes, he was near the referee."
He said: "When I did this against Liverpool, people told me not to do it.
"I said I was sorry and made a mistake. Today ...
"Maybe if you look at it."