Mancini felt Rooney pressured referee Chris Foy into showing a red card after Kompany was penalised for a two-footed challenge on Nani with just 12 minutes of an explosive FA Cup tie gone.
Rooney used Twitter to express his thoughts on the matter.
The England forward wrote: "Funny how people think i got kompany sent off. Im not ref. i didn't give red card. But it was a clear red card. 2 footed tackle."
He protested his innocence in a later interview with the Sun, saying: "I didn't wave any imaginary card. I clearly pointed out, and a few other players did as well, that it was a two-footed tackle. It was down to the ref to send him off.
"As professional footballers, when you leave the ground and go in two-footed we've now been told by the referees it's a red card. Refs come and see us before the season starts. I felt Kompany had done that."
Mancini himself was criticised for waving an imaginary card after an incident in his side's defeat of Liverpool last week.
The Italian felt Rooney's actions were of a similar nature.
"It was not a red card," Mancini said. "Rooney told him his decision.
"When I did this against Liverpool, people told me not to do it.
"I said I was sorry and made a mistake."
With their influential captain now facing a four-match suspension, City are intending to appeal against Kompany's sending off.
The club have until Monday afternoon to lodge their appeal with the Football Association and if they do a hearing will take place on Tuesday.
If it proves unsuccessful, City will have to make do without Kompany for both legs of their Carling Cup semi-final with Liverpool and Premier League games against Wigan and Tottenham.
With Kolo Toure away at the African Nations Cup, that would leave Joleon Lescott and Stefan Savic as Mancini's first-choice centre-half pairing.
The Premier League leaders' squad, despite its undoubted quality, is already starting to look stretched with Yaya Toure also away and strikers Edin Dzeko and Mario Balotelli recently injured.
One option to alleviate the problem could be to restore Nedum Onuoha, who has been expected to leave, to first-team duty. A recall for Dedryck Boyata, who is currently on loan at Bolton, has also been suggested.
Yet Mancini is confident Kompany will be available for the forthcoming fixtures, starting with the visit of Liverpool on Wednesday.
He said: "We will appeal. I am sure we will win."
Without Kompany, City were beaten 3-2 by United, despite a stirring fightback from 3-0 down, and saw their FA Cup defence end at the third-round stage.