The Italian was angry that his captain faces four-match ban but insisted he was 'proud' of a performance which he believes proves his side can win the Premier League title
City captain Kompany was sent-off in the 12th minute at the Etihad Stadium for a two-footed challenge on United winger Nani as Sir Alex Ferguson’s side booked their place in the fourth round with a 3-2 victory.
Mancini refused to criticise referee Chris Foy for fear of a touchline ban but was clearly furious as he faced up to the prospect of losing Kompany for four matches through suspension.
“The red card for Vinnie? It’s impossible. I will appeal,” Mancini told reporters.
“I am sure that we will an appeal, I'm sure. If you can explain to me why he showed a red card...
“I think every man can understand if it was correct or not. But now it's finished.
“I don’t want to talk about the referee because I want to stay on the bench for the next game.”
United took a 3-0 lead in the first-half thanks to Wayne Rooney’s double either side of a Danny Welbeck volley, but 10-man City fought back in the second-half and nearly claimed a draw after goals from Aleksandar Kolarov and Sergio Aguero.
Mancini made a double substitution at the break and was ‘proud’ of the way his players performed as City avoided a humiliation similar to the 6-1 thrashing they gave United in the Premier League game between the sides in October.
The Italian insisted the spirit showed by his side proved City, the Premier League leaders, can win their first title in 44 years this season.
“I think today is important for us for the league,” Mancini added.
“I think now we can win the league. United is a top squad in England and if we play like this afternoon against them with 10 players and we have the same attitude, the same strength in every game, we will win the league.
“I said at half time that we needed to defend very well and we defended very, very well.
"We didn't concede any chances to United in the second half - this is not easy with 10 players against United.
“At Old Trafford with 10 men they lost 6-1, and they played for 40 minutes with 10 players. We played for 80 minutes with 10 players and we didn't concede any chances in the second-half.
“We scored two goals, we had other chances to score. I think for us – who needed to improve - it was a fantastic performance.”
Mancini also joked of his surprise at Paul Scholes’ shock comeback from retirement after the United legend played the final half an hour as a substitute.
Mancini said: “I thought ‘David [Platt], go on the bench please!' Paul Scholes is a fantastic player but it was strange to see him on the bench. Incredible.”