Roberto Mancini's side defeated Tottenham 2-1 on Sunday, with another late goal courtesy of Edin Dzeko rescuing all three points for the club, which keeps them two points adrift of league leaders and fierce rivals Manchester United.
The 27-year-old believes the club will have to work even harder this season as a bigger scalp for the rest of the league, but acknowledges that it is part of the territory.
Zabaleta told reporters: "We have come a long way in the last four years and the expectations have changed.
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"You are up there to be shot at and we take it all on the chin.
"It happens at other clubs. It's just the way things are."