Director of football Txiki Begiristain said City will have to show a fighting spirit.
He said: "You can never make excuses - in football never.
"It won't be easy but we have to fight. The champions Bayern are there, we also need to be careful with CSKA Moscow and also Plsen. We have to be careful with all of them."
Plzen is City's first destination in Group D on Tuesday, September 17. The home match against Bayern Munich comes next with CSKA Moscow (A), CSKA Moscow (H), Plzen (H) and Munich (A) completing the fixture list.
Arsenal face a daunting task after being drawn alongside last season's runners-up Borussia Dortmund, Rafael Benitez's Napoli and Marseille in the Champions League group stages.
The Gunners, who qualified after completing a comprehensive play-off win over Fenerbahce this week, were placed in the tough-looking Group F at UEFA's draw in Monaco.
Dortmund coach Jurgen Klopp, whose side failed to beat the Gunners in either of their 2011 meetings, said: "It's a fantastic, even group. It includes four teams who are all capable of going through.
"The fact is, we've got a bit of a score to settle with Arsenal and we also have some revenge to get on Marseille.
"I've never been to Naples and I'm already looking forward to the atmosphere there. It's going to be very, very exciting."
Arsenal open in Marseille on Wednesday, September 18 and then face Napoli (H), Dortmund (H), Dortmund (A), Marseille (H) and Napoli (A).
Celtic, who famously beat Barcelona last season, will face the Catalan giants again along with two other former winners in Group H in AC Milan and Ajax.
Manager Neil Lennon told Sky Sports News: "I think it is the best and the worst draw we could have got.
"In terms of glamour I don't think it comes any better than Barcelona, Ajax and AC Milan.
"In terms of football it is probably the most difficult group we could have got.
"But I think the hard work was really done last night and we can go and enjoy the tournament now."
AC Milan visit Parkhead on Wednesday, September 18 for Celtic's opening contest.
A trip to Barcelona follows on matchday two with the rest of the fixtures out as Ajax (H), Ajax (A), AC Milan (H) and Barcelona (A).
Chelsea face two of the sides they conquered en route to last year's Europa League success in Basel and Steaua Bucharest, as well as Schalke, in Group E.
The Blues' chief executive Ron Gourlay thinks the club will be boosted by Jose Mourinho's return as manager.
He said: "Jose has come back to continue the evolution of the football club. Jose went on to be very successful after he left and Chelsea continued to be too so we are now looking to continue that evolution.
"We have a very, very young squad of players now and that's very important for the next five or six years.
"We are very, very happy with the team and if the window closed today we would be fine. We have started the season very well and we are very happy with how things are going."
Basel visit Stamford Bridge for Chelsea's first match on Wednesday, September 18 with games against Bucharest (A), Schalke (A), Schalke (H), Basel (A) and Bucharest (H) following.
David Moyes' Champions League bow with Manchester United will come against Shakhtar Donetsk, Bayer Leverkusen and Real Sociedad in Group A.
The Red Devils open their campaign against Leverkusen at Old Trafford on Tuesday, September 17 before the fixtures see them face Shakhtar (A), Sociedad (H), Sociedad (A), Leverkusen (A) and Shakhtar (H).
Real Madrid have been drawn in the same group as Italian champions Juventus as they begin their latest hunt for an elusive 10th European Cup crown having last tasted success back in 2002.
Galatasaray and FC Copenhagen are the other sides in Group B.
Group G consists of three clubs who have lifted the UEFA Cup/Europa League in recent years with Atletico Madrid (2010 and 2012 winners), Porto (2011) and Zenit St Petersburg (2008) drawn together along with Austria Vienna.
French Ligue 1 champions Paris St Germain are in Group C with Benfica, Olympiacos and Anderlecht.
Champions League group-stage draw:
Zenit St Petersburg
Matchday one - September 17-18
Matchday two - October 1-2
Matchday three - October 22-23
Matchday four - November 5-6
Matchday five - November 26-27
Matchday six - December 10-11