Defender Kompany was sent off for a tackle on Nani 11 minutes into the FA Cup third-round tie.
As the City captain has already been sent off for a straight red card offence once this season, he is facing a four-match ban unless he can overturn the suspension.
"We will appeal," said Mancini.
"I am sure we will win."
Mancini opted not to criticise referee Chris Foy.
However, he thinks little can be read into the defence offered almost immediately by former top-flight official Dermot Gallagher, who claimed Foy had got it right.
"This is normal. If I talk about the players, I defend the player. The referee is the same. He defends the referee," said Mancini.
"I don't want to talk about the referee because I want to stay on the bench for the next game.
"But I think it is impossible."
Kompany stands to miss both legs of the Carling Cup semi-final with Liverpool, in addition to Premier League games against Wigan and Tottenham.
Sir Alex Ferguson pulled no punches afterwards, claiming it was the right decision and that Kompany has been guilty of similar transgressions before.
"It was a sending-off," said the Manchester United boss.
"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."
Although he did not refer to the red card, it seemed Kompany was equally unimpressed, claiming City were "the moral victors".
"The fans, the players and every single person involved with Man City FC were incredible today [Sunday]. Definitely the moral winners of this game," said the Belgian on Twitter.
And Aguero added: "I seldom try to find excuses or comment on the referees. But the unfair expulsion of '@VincentKompany' conditioned the whole game."
However, from an FA official came a warning for City not to get their hopes up.
"On red card appeals note the panel not asked to give their view on incident, simply asked whether referee made a serious and obvious error," he said