The victory in North London means that second-placed City are now seven points behind league leaders Manchester United, but Mancini is adamant that his side can catch their rivals.
"United are really strong and in this moment they are playing very well, but the season is long. It is important for us to be close to them at the end," said Mancini.
"We had some pressure [to win at Arsenal], but seven, eight or nine points doesn't change much. It is difficult to emulate last season but sometimes it can happen.
"I don't think we deserve to be seven points behind, but we are there and we need to play well. We have to keep strong if we want to have another chance."
City host Fulham in their next league match on Sunday.