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."