The City captain was dismissed after just 12 minutes of a pulsating third-round tie at the Etihad Stadium, which United eventually won 3-2, after a challenge on Nani.
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.
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."
Mancini referred to last week's 3-0 win over Liverpool, when he wanted Martin Skrtel sent off for bringing down Yaya Toure.
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."
Kompany will now miss both Carling Cup semi-final legs against Liverpool, the first of which is on Wednesday, as well as Barclays Premier League clashes with Wigan next week and Tottenham on January 22.
The dismissal carries an extra game suspension above the usual three because it is Kompany's second sending-off of the campaign.
Mancini, however, is confident City will succeed in their attempts to have the ban overturned.
He said: "We will appeal. I am sure we will win.
"I think Vinny will play against Wigan."
United boss Sir Alex Ferguson pulled no punches after the game, claiming Foy made the right decision and that Kompany has been guilty of similar transgressions before.
Ferguson said: "It was a sending-off.
"It was a two-footed tackle. I have seen him do it before.
"He has got off with it in the past. But if Nani gets caught, he has a problem. It was a real bad one."