City went ahead through Edin Dzeko after a goalless first half but Aron Gunnarsson's equaliser and two Fraizer Campbell goals, both from corners, gave the Premier League new boys a 3-1 lead.
Despite Alvaro Negredo pulling a goal back for City, it was not enough to deny Cardiff their first three points of the season and the right-back admits his side have a weakness at set-pieces.
"We didn't defend well and it cost us the game," said Zabaleta in The Sun.
"We were the better team - but the only differences were the set-pieces where we conceded silly goals.
"We are all very disappointed that we lost, because we created enough chances to get some points.
"Sometimes we will find teams that will take their chances from dead balls - that's their hope of winning games against us."
Zabaleta suggested that the change in defensive policy under new manager Manuel Pellegrini is taking time for the team to adapt to.
He added: "It has changed for us. Last season we were marking zonally and now it is individual marking and sometimes it is hard - but Campbell was very strong in the air.
"It is a worry to concede two goals from set-pieces - it's hard to take."
The 28-year-old insists City must now bounce back when they face another of the promoted sides in Hull City at the Etihad on Saturday.
"We didn't play like we did in the last game and were a bit static in the first half against Cardiff," he said.
"They did well defensively and didn't give us many chances. The boss said we need to learn from our mistakes - now we must come back strongly against Hull and get three points."