Sergio Aguero struck the winner late on at Emirates.
Mancini was happy with the result, the club's first victory at Arsenal in 28 attempts.
"We had a chance seven minutes from the end and we scored. It was a great goal. A great counter-attack," he said.
"I don't think that Arsenal had a lot of chances, I think we played well.
"It will be better to win here in the Premier League but it is a good feeling because we are into the semi-finals of the competition.
"We have a strong squad - all of the top teams have a good squad and can change eight, nine or 10 players. It is normal for the Carling Cup to change.
"December and January will be crucial months because we play tough games and we play every three days. After January we can talk about whether we can win things or not."