City are facing a familiar battle to qualify from their group after collecting just two points from their opening three matches in this season's competition.
Their latest disappointment came as they surrendered a two-goal lead to draw 2-2 with CSKA Moscow on a freezing night in the Russian capital.
CSKA's late equaliser did come in controversial circumstances, as City conceded a disputed penalty four minutes from time, but Zabaleta felt the overall display was not up to standard.
The Argentinian said: "It was really painful for everyone to only draw
It's not good enough for this team to only draw here.
"We are much better than we are showing in this competition.
"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."
City looked to be on course for a comfortable win as they took a 2-0 half-time lead through Sergio Aguero and James Milner, who also hit the post.
But CSKA rallied after the break to level through substitute Seydou Doumbia and the same player won the late spot-kick when he fell under a challenge from Aleksandar Kolarov
Bibras Natcho converted.
City were also aggrieved they did not get a penalty when Edin Dzeko seemed to be impeded in the first half but Zabaleta felt the English champions let standards slip.
He said: "It's so frustrating
We were 2-0 up at half-time and that was a good result for us.
"It's not the first time this has happened and it's something we need to sort out as soon as possible.
"Sometimes you can win games even when you are not playing at your best and I think we find that hard.
"We were not very lucky with the penalty decision
I think there was a penalty on Dzeko that wasn't given in the first half
The referee should not give that penalty to them if he doesn't give ours."
City are now seven points behind Group E leaders Bayern Munich and look to be in a three-way battle for second spot with CSKA and Roma.
Zabaleta said: "Now it's really hard for us
For us to go through it is very complicated.
"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.
"We will see what the other results are but the most important thing was that we get our results and what we did was not good enough."
Source : PA
Source: PA