Italian boss Mancini felt Rooney influenced referee Chris Foy into showing defender Kompany a red card for a two-footed challenge on Nani just 12 minutes into Sunday's incident-packed third round clash.
But the England striker, who scored goals either side of Kompany's exit in a first half where Danny Welbeck also netted for United, defended himself on Twitter on Monday by saying: "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."
Mancini compared the actions of Rooney, seen speaking to Foy after Kompany's tackle and before the sending-off, to his own in waving an imaginary red card during City's win over Liverpool last week.
"It was not a red card," Mancini said after a defeat that saw City's defence of the FA Cup they won last season end after just one match.
"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."
As City captain Kompany now faces a four-match suspension, the Premier League leaders are set to lodge an appeal against his red card before Monday's deadline expires.
If an appeal is rejected, City will be without Kompany for both legs of their League Cup semi-final with Liverpool and Premier League games against Wigan and Tottenham Hotspur.
With Kolo Toure on African Nations Cup duty, that would leave Joleon Lescott and Stefan Savic as City's first-choice central defensive duo.
However, Mancini was confident City would get Kompany's ban overturned, in which case the defender would be available for Wednesday's visit of Liverpool.
"We will appeal. I am sure we will win," he said.