Zabaleta has witnessed City's rapid progress over the past five years at first hand, having signed the day before the club's Abu Dhabi-funded takeover in 2008.
Winning the FA Cup in 2011 proved the first tangible reward for a huge investment in players and that was followed by success in the Barclays Premier League the following year.
Now City want to make an impression in Europe and, after two Champions League group-stage failures in the past two seasons, they are now eyeing a last-16 place for the first time.
Making such progress was a minimum objective for new manager Manuel Pellegrini this season and victory over CSKA Moscow at the Etihad Stadium this week could see him achieve it.
Zabaleta said: "I think in the last four or five years this club has been improving incredibly.
"We know that the owners been spending much money to try and build a good team and try to have one of the best teams in Europe.
"Sometimes it takes time. We won the FA Cup and the Premier League, (but) the Champions League is a different competition. You play against the best teams in Europe.
"It is time for this club to take a step forward.
"If we can qualify for the next round, it will be great for this club.
"Hopefully in the next few years we can be one of the top clubs in Europe."
Although City were taught a footballing lesson by Bayern Munich last month, their victory over CSKA in the Russian capital a fortnight ago gave them a grip on second place.
A repeat win will see City go through, providing Bayern avoid an unlikely defeat against Czech minnows Viktoria Plzen.
Zabaleta said: "I think we have a great chance to go through to the next stage if we can win.
"We don't expect an easy game because we know they have some very good individual players, especially up front, they are good on the counter-attack.
"It is true, when we look at the last two seasons and our performance in the Champions, it was really poor.
"All the players are really focused to try to improve our performance in the competitions and winning tomorrow will be a step forward."
Striker Edin Dzeko, meanwhile, has reacted with anger to a report claiming he complained about former manager Roberto Mancini to chairman Khaldoon Al Mubarak.
Mancini was sacked in May amid rumours of disharmony among the squad.
Dzeko says he is "angry" about any suggestions he was involved in a dressing room revolt and that a TV interview he gave in Bosnia has been misinterpreted.
Dzeko tweeted: "It says I confess to being part of a dressing room revolt and that I turned on Mancini.
"I did not say these things when I spoke to Bosnian TV - the context is changed in the article.
"Also some of my real words have been interpreted badly."