Martin Demichelis' red card proved costly as Lionel Messi scored the resulting penalty – which City felt should have been a free-kick just outside the area – and Dani Alves rubbed salt into the wounds with a second goal late on.
The Spanish champions will be expected to finish off the job in the second leg next month, but Zabaleta is refusing to rule his side out of the tie and will be going to Catalunya with the belief they can progress.
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"We need to have some belief and do better in Camp Nou.
"We still have 90 minutes to try to do something and we should go there and try as hard as we can to do something."
The Argentina international had no arguments with referee Jonas Eriksson's decision to dismiss Demichelis, but was aggrieved that the Swedish official pointed to the spot when the centre-back upended compatriot Messi.
"I'm a bit disappointed at the result. It was not the same, 2-0 as 1-0," he added.
"The referee made a few mistakes in his decisions. It should never have been a penalty as it was very clear it was at least one metre outside the box.
"I think it is a red card because Demichelis was last man and it was a foul on Messi, but it was a free-kick and not a penalty.
"They should have done better on that decision. That is football sometimes and we should respect decisions, but in this kind of game one mistake makes a big difference."