City failed to win a game in the competition last season, picking up just three points as they finished bottom of a tough group that featured Real Madrid, Borussia Dortmund and Ajax.
The Argentina international says the club have learned from their experiences in the competition though, and feels they will put on a better showing under new manager Manuel Pellegrini.
"I think it is another chance for this club, for this team, to do better in the Champions League," he said ahead of City's clash with Viktoria Plzen on Tuesday.
"From what happened the last two years in the Champions League, I think we learned and hopefully we will do better."
City's first involvement in the Champions League was in the 2011-12 campaign, when they finished third in another difficult group that contained Napoli, Bayern Munich and Villarreal.
This season, City again meet Bayern, but with Plzen and CSKA Moscow also in Group D, Zabaleta believes they have a better chance of progression.
"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," he said.
"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."
Pellegrini will take charge of his first European game as City manager at the Doosan Arena.
The Chilean reached the semi-final of the competition with Villarreal in the 2005-06 season, while he also guided Malaga to the last eight last season.
And Zabaleta has backed the experienced manager to guide City to European success as well.
"He is a manager with good experience in the Champions League," he continued.
"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."
Pellegrini could welcome back captain Vincent Kompany for the game in the Czech Republic.
The Belgian has been out of action for over a month after injuring his groin in a 4-0 Premier League win over Manchester United.
