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 salted into the wounds with a second goal late on.
The Spanish champions will be expected to finish off the job in the second leg at Camp Nou next month, but defender Zabaleta has not given up hope of reaching the quarter-finals.
He told reporters: "Now we need to play another 90 minutes and it will be very difficult, but nothing is impossible in football.
"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.
He said: "I'm a bit disappointed at the result. It was not the same, 2-0 as 1-0.
"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."
The two sides meet again in the second leg on March 12.
