City will make their Champions League debut against Napoli on Wednesday evening and also tackle Bayern Munich and Villarreal in the group phase.
In addition, the club's stunning 100 per cent start to the Premier League season has drawn parallels with the style of football played by current European champions Barcelona.
However, following Saturday's comprehensive 3-0 win over Wigan, Mancini was keeping realistic about City's prospects following the progress the club have made in recent seasons.
"I understand why people are getting excited but it is still early for us," said Mancini.
"Yes, it's our target to improve, to win the Premier League and Champions League in the future.
"But let's see what happens in May. This group of players has only been together for two months and we need time.
"Of course, playing in the Champions League was all part of the project. But we are actually in the competition sooner than I thought we would be.
"The club has bought good players and we worked very hard and for these reasons we deserve to be where we are. But we still need to improve.
"We can say we want to win the Champions League because all the teams who enter it want to win it.
"But for us now it's important we reach the second stage. We're in a hard group where anyone could finish top or bottom.
"Remember the Champions League is different from the Premier League. If you lose a game in the domestic championship, you have time to recover.
"If you lose a game in the Champions League, you don't have that opportunity."