City have failed to progress beyond the group stages of Europe's premier competition over the last two years, and they failed to win a single game last season in a group including Real Madrid, Borussia Dortmund and Ajax.
They have been given a kinder draw this term despite being in Group D with defending champions Bayern Munich, with Viktoria Plzen and CSKA Moscow providing the other opposition.
Ahead of Tuesday night's clash with Plzen, 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.
"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."
New City manager Manuel Pellegrini boasts a good record in the competition, reaching the last four with Villarreal and almost guiding Malaga into the semi-finals last season.
Zabaleta added: "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."
You can watch Viktoria Plzen v Manchester City live on Sky Sports 2HD at 7pm