Mancini was full of praise for his players who recovered from the early sending-off of Vincent Kompany and the concession of three first-half goals to make their neighbours sweat on the result until the very end of a gripping third-round match.
"I am disappointed with the result but I am very happy with my players for their performance," Mancini told a news conference.
"We defended very well in the second half, they did not have a chance and we scored two goals. It is not easy to play with 10 players against United."
Mancini was very optimistic his team could now go on to win the Premier League title despite suffering their first home defeat for over a year.
"After the way we played and the character we showed I think we can win the league now," he said. "To play like that against a team like United with only 10 players is very good."
United manager Sir Alex Ferguson was annoyed that his team had been forced to endure a worrying final few minutes after allowing City back into the match.
"It was a careless performance by us," he said. "We made mistakes in the second half and they punished us. That's what can happen if you make mistakes."
Ferguson said his game plan had worked perfectly in the first half.
"We set up to hit them on the break and that's what we were able to do with the three goals," he said. "The sending-off changed the game but I thought it was the correct decision. He's gone in two-footed."
Ferguson said United had made City look better than they were.
"The problem was being 3-0 up at half-time the players thought they were through and took their foot off the pedal," he said.
