City thought they had snatched a late winner after battling back from 2-0 down to 2-2 against Ajax at the Etihad Stadium but Sergio Aguero's celebrations were cut short by an offside flag.
And in a frantic finish, City were then denied an injury-time penalty after Ricardo van Rhijn held back Mario Balotelli as referee Peter Rasmussen blew the final whistle.
Emotions boiled over as Balotelli protested and manager Roberto Mancini, in actions that could land him in disciplinary trouble with UEFA, came onto the field to confront the official.
Zabaleta said: "We knew it was not offside, and on the penalty we were frustrated by the decision.
"We were frustrated and disappointed by the referee's decisions, but in the end you can do nothing."
City, with just two points from four games, now need other results to fall in their favour to have any hope of reaching the knockout stages.
They will also need to win their final two Group D games against Real Madrid and Borussia Dortmund but Zabaleta has vowed to fight to the end.
The Argentina international said: "Now it's going to be really difficult, but mathematically we are still in with a chance, so we need to fight.
"The next game (against Madrid) is really important, against probably one of the best teams in Europe at the moment, so it's going to be exciting."
City were stung early on as Siem de Jong scored twice at corners inside the opening 17 minutes.
Yaya Toure pulled one back with a fine volley soon after and Aguero equalised 16 minutes from time.
City continued to press but Aguero was frustrated after Aleksandar Kolarov was ruled to have strayed narrowly offside before crossing for what seemed an 88th-minute winner.
The controversy involving Balotelli, who had his shirt and his arm pulled close to the additional official behind the goal, compounded their anguish.
Zabaleta said: "At the end the team showed very good spirit.
"We conceded two early goals. It was difficult but we pushed them hard in the second half.
"We were unlucky with the last goal because I think Kolarov was onside. I think the referee and linesman were wrong.
"When you fight to the last minute to get the three points - I think we deserved the third goal."