The Premier League champions were held to a 2-2 draw by Group E rivals CSKA Moscow on Tuesday night, a result which leaves them on just two points after three games in the current campaign.
City now face an uphill battle to reach the next round of the competition, and Zabaleta insists that the performances have not been good enough.
"Now it's really hard for us," the Argentine told reporters. "It was really painful to only draw. It's not good enough for this team to only draw here.
"We're much better than we're showing in this competition. For us to go through now, it's very complicated. It will be hard for us to qualify for the round of 16 with only two points from three games and that's not good enough.
"We still have a chance and we will do everything to qualify, but if you don't win games you can't get through the group. And we haven't done that yet."
City return to Champions League action against CSKA at the Etihad Stadium on November 5.