City's first two ventures into Europe's elite competition have ended prematurely at the group stage.
Last season's campaign was particularly underwhelming as they failed to win a game, albeit from a tough group including Real Madrid, Borussia Dortmund and Ajax.
This year the draw appears kinder with the task of taking on European champions Bayern Munich offset by games against the lesser-fancied Viktoria Plzen and CSKA Moscow in Group D.
The minnows of Plzen, the Czech champions, are their first opponents at the modest Doosan Arena on Tuesday evening.
Argentina right-back Zabaleta said: "I think it is another chance for this club, for this team, to do better in the Champions League.
"From what happened the last two years in the Champions League, I think we learned and hopefully we will do better.
"It is not an easy group - I am not saying this - but maybe if you compare this group with the last two years, it is a bit better.
"We believe in this team and I think we have got a great chance to qualify for the next round."
City have been unable to win the first match of either of their previous two campaigns.
In 2011 they were held to a 1-1 draw by Napoli at the Etihad Stadium and last year they surrendered a lead to lose at Real Madrid. Last season they also lost all three of their away games.
Zabaleta, 28, said: "It is important to win tonight, to try to get three points.
"To start winning is important because then we have got Bayern Munich at home."
City's disappointing Champions League showings were one of the reasons the club decided to part company with their 2012 Barclays Premier League-winning manager Roberto Mancini last season.
His replacement Manuel Pellegrini boasts good pedigree in the competition.
Last season, his Malaga side got within moments of securing a place in the semi-finals - a stage the Chilean previously reached with Villarreal.
Zabaleta said: "He is a manager with good experience in the Champions League.
"He did well with Villarreal, and also with Malaga. Now it is a different experience for him, with a new team. Hopefully we can do well."
City are hoping captain Vincent Kompany will be fit to return after the defender travelled with the squad to the Czech Republic.
Kompany has been out since limping out of the first game of the season against Newcastle with a groin injury.
The Belgian has been training as normal for the last three days and his potential return would give Pellegrini a lift ahead of next weekend's derby against Manchester United.
Pellegrini said: "We will see if he is 100 per cent. If he is, of course he will play.
"I think he will be 100 per cent, but if he is not he will not play."
Playmaker David Silva did not travel after missing last weekend's game at Stoke with a thigh injury.
- Sports & Recreation
- Bayern Munich
- Real Madrid
- Viktoria Plzen
- Borussia Dortmund