Yaya Toure fired City into their first final since 1981, where they will play the winners of Sunday's clash between Bolton and Stoke. Mancini's men will be strong favourites to claim their first trophy since the 1976 League Cup at Wembley next month, but the Italian claimed the final would be even tougher than Saturday afternoon's 1-0 victory.
A delighted Mancini said: "I'm very happy. I'm very happy for our supporters. They deserve to have a day like this. We mustn't forget we play another game. We won only the semi-final."
City's travelling fans must have been fearing the worst after an opening quarter dominated by United which saw Dimitar Berbatov produce two glaring misses.
Mancini added: "It's difficult to play against United. They're used to playing this (type of) game every year. For us, it was the first time after a long time.
"Maybe we had some fear in the first 20-25 minutes. In the last 10, 15 minutes of the first half, we started to play high, we started to press.
"In the second half, we dominated the game. I am happy because we had fantastic spirit and we beat a team like Man United."
It would not be a Manchester derby without controversy and both sides duly delivered as Paul Scholes was sent off for a thigh-high tackle on Pablo Zabaleta and Mario Balotelli was involved in some ugly exchanges with United players on the final whistle after celebrating in front of opposition supporters.
Mancini said of the latter incident: "I didn't see it. I want to wait because every time, 'It's Balotelli's fault'."
When the incident was described to him, Mancini joked: "We can put him in jail? Next week, we can put him in jail for this."
Source: PA
Source: PA