Argentine defender Zabaleta was sent off at the Nou Camp for two bookable offences, picking up his second booking for his protests to Lannoy over his failure to award City a penalty when Edin Dzeko appeared to be felled by Gerard Pique inside the box.
Barcelona also had a strong penalty appeal of their own waved away in the first half, while the home side had a goal controversially ruled out for offside even though replays showed Jordi Alba was onside before he crossed for Neymar to score.
Zabaleta was insistent that City should have had a penalty for the Dzeko incident and he claims he is in the dark as to why he was sent off.
"It was very clear," Zabaleta said. "I think Pique was behind me and made the tackle on Dzeko and the referee was only two metres away from that.
"I don't know why I was sent off. I went to him to talk to him in a good way.
"I was a little bit angry to him because he didn't give a penalty but I have always been very respectful to him.
"I am frustrated. I think it was a shocking decision.
"Sometimes in the game you are nervous because you are trying to get the result, and sometimes shocking decisions by the ref make you a bit angry."
Zabaleta also felt City should have received a free-kick before Barcelona opened the scoring through Lionel Messi, feeling Dzeko was fouled in the build-up to the goal.
"It was also a foul against Dzeko just before Barcelona's first goal," added Zabaleta. "He held the ball and turned, and Pique had hold of his shirt, and the ref gave a free-kick to Barcelona."
"I am disappointed but also very proud of the team because I think we played a fantastic game.
"We tried from the beginning until the end, should have scored first and had more chances in the game."