Nonetheless, he believes they do have it in them to go on and win the competition.
City, beaten 3-2 by Real Madrid at the Bernabeu in their Group D opener last month, are looking to get their European season kick-started on Wednesday when they take on German champions Borussia Dortmund at the Etihad Stadium.
With Dortmund having begun with a 1-0 win over Ajax, the pressure is on the Blues to secure all three points if they are to avoid a repeat of their maiden Champions League campaign last term, which ended in failure to qualify from another difficult group.
While acknowledging the club are relatively inexperienced at this level, Mancini accepts there is a considerable weight of expectation on City to make major strides on the European stage, and has stressed the importance of his players cutting out the kind of mistakes he felt allowed Real to snatch victory against them.
The Italian is optimistic, though, that if City do manage to up their game and make it beyond the group stage, there is no reason why they cannot then go all the way.
"This is the second year for us in the Champions League and the second year that we got the worst group," Mancini said.
"Like we have improved (over the years) in the Premier League, we need time to improve in the Champions League, but we don't have a lot of time - only five more games, and we need to improve quickly.
"We need to not concede easy goals to drop points like we did against Real Madrid. If we want to go through, we need to improve very quickly."
Asked if he felt he was still learning about Champions League football on a personal level, Mancini said: "I don't need to learn.
"The Champions League is a difficult competition, but football is the same. It doesn't change - it is still 11 players against 11.
"The problem is that you are always playing against the best team from another country and every game is difficult.
"I hope I can improve my record in the Champions League, and I think we have arrived at the time where we can win the Champions League."
Dortmund coach Jurgen Klopp, meanwhile, feels his team have taken valuable lessons from their experiences in the tournament last season and has made it clear they are looking to get something out of Wednesday's clash.
Dortmund returned to the competition last term for the first time in eight years, but had a disappointing time of it, finishing bottom of their group after suffering four defeats in their six games.
The German outfit are back again in 2012-13 after securing a second successive Bundesliga title under Klopp, who feels they are wiser for their experiences in Europe of a year ago.
So far this time out they have made a positive start in Group D by beating Dutch league winners Ajax 1-0 at home, and while the 45-year-old is expecting Wednesday's assignment to be a tough one, he is optimistic Dortmund can emerge from it with a positive result.
Asked if he felt his side were getting used to the Champions League, Klopp said: "We have taken a step forward and we have learned a lot from defeats in past Champions League campaigns.
"Tomorrow [Wednesday] will be a different question. But at the end of the day, we have come here to get something out of the game.
"We are fully focused, we want to get a result tomorrow [Wednesday] night and that is what we will be playing for."