City have made another disappointing start in the competition having collected just one point from their opening two matches in Group D.
Alarmingly, according to UEFA statistics, they have allowed 50 attempts on their own goal during their opening loss at Real Madrid and in their draw against Borussia Dortmund last time out.
It leaves them heading into the first of their back-to-back games against Ajax in the Amsterdam Arena anxious for a result.
Mancini said: "It is better that we don't concede a lot of shots, but we played against Madrid in Madrid, so it is difficult not to concede chances.
"We had a bad game against Dortmund, but it is important we don't give away so many chances to score.
"This group is very difficult. We haven't started very well, tomorrow [Wednesday] will be a difficult game.
"People think it will be easy, but Ajax have a good young team and will play well. It is more difficult away from home.
"We can't think before the game about not winning. We have to think about winning this game."
City found themselves in a similar situation 12 months ago after managing just one draw in games against Bayern Munich and Napoli.
They went on to beat Villarreal twice in succession but still failed to progress from the group stage despite ending it with 10 points.
That meant that, despite their status as Barclays Premier League champions, City were again seeded in a difficult group - one comprising domestic champions - this season and they must advance to improve their co-efficient.
Mancini has no doubt his players are good enough to reach the last 16 but it is a case of obtaining the results.
The Italian said: "It is frustrating. We are here and every group game is difficult in the Champions League.
"We should continue our way and if we play like this, we will win.
"We don't have experience as a club, but all of our players have Champions League experience.
"Maybe as a club, we need more experience, but we have good players and that's why we should be in the second stage.
"It is not easy because you need luck in this competition when you have the draw for the group.
"We want to play for a better seeding. We started the group so-so, but we still have a chance to go through - but we must take our chance."
City will have to achieve their aims in Holland without playmaker David Silva, who remains out with a hamstring injury and has not travelled.
Defender Maicon and midfielders Jack Rodwell and Javi Garcia are also missing.
Those that did make the trip trained at the Amsterdam Arena on the eve of the match.
That represented a break from Mancini's usual European routine as the manager usually prefers to train in Manchester in the morning before travelling.
After previous disappointments, it was suggested to Mancini he might be trying something different but he insisted it was nothing significant.
Speaking at his pre-match press conference, he said: "Some players wanted to see the stadium because it is fantastic and they wanted to train here. Only this."
It was also put to Mancini by a Dutch journalist that he is a "lucky" manager because his club's vast spending power allows him to buy almost whoever he wants.
Mancini said: "I am very lucky because I work for a fantastic club - but this is not true."
Mancini was non-committal on when asked about his strikeforce and whether Edin Dzeko might have done enough to earn a starting spot.
Dzeko is the club's top scorer this season with six goals, five of them after coming off the bench, including last weekend's vital double against West Brom.
Mancini said: "It is always difficult. When you have four strikers like Mario (Balotelli), Sergio (Aguero), Carlos (Tevez) and Edin, you can't play them all.
"Dzeko was fantastic against West Brom, but we will decide tomorrow [Wednesday]."