While wealthy owner Sheikh Mansour's backing has successfully transformed the club into a Premier League powerhouse, forays into Europe's premier club competition have led only to a string of disappointments.
But Zabaleta believes City are now ready to justify their domestic billing and compete with the continent's best.
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"We know that the owners have spent so much money to try to build a good team and to try to be one of the best teams in Europe.
"We know it takes time. We won the FA Cup, we won the Premier League, but the Champions League is different.
"You play against the best teams and it has not been easy, but now we are very positive and everything is set for this club to take a step forward.
"If we can qualify for the next round, it would be great for this club. We are still improving and hopefully in the next few years, we can be one of the top clubs in Europe."
City are currently second behind Bayern Munich in Group D, but a win against CSKA Moscow on Tuesday will put them in a strong position to reach the knockout stages for the first time at the third attempt.
"We have a great chance to go through if we can win," Zabaleta continued. "It is time for us to win. The last two seasons have been really poor in the Champions League and we are all focused on improving.
"We want to take a step forward and qualify for the next round."