City's apparently quickening title charge was slowed and their free-scoring attack blunted as the Londoners claimed a 1-0 win at the Etihad Stadium.
The result prevented City moving back to the top of the Barclays Premier League and saw Chelsea pull level with them in second, two points behind leaders Arsenal.
It also ended their formidable home run, having won all 11 previous league games at Eastlands, and was the first time they had not scored at the ground since November 2010.
Zabaleta said: "We were a little bit frustrated by the result but this is football. Sometimes you can lose games.
"We can learn from mistakes and we see how difficult the Premier League is at the moment. Every game is very difficult.
"We need to keep calm. I think the manager is clever enough to work during the week and show to us on video what we did wrong and try to do well next game.
"We still have a chance in four competitions. We have important games coming up in February.
"We need to have a good rest now and be ready for Saturday. That is going to be another tough game, Norwich away."
City host Chelsea again in the FA Cup fifth round on February 15, three days before Barcelona visit in the Champions League.
Before that they have Premier League games against Norwich and Sunderland, who are also their Capital One Cup final opponents on March 2.
Zabaleta said: "It was one of those games that we didn't do our stuff.
"It was an important game for us to get three points and be back on top of the league.
"We need to think and be positive now and review the game, just to see all the mistakes and try not to make them again.
"Sometimes when you lose one game it is terrible, but we must be stronger than ever.
"We know we are only two points behind Arsenal and there is still a long way to go.
"We have got 14 games more to the end of the season. We need to be positive."
City started with confidence as Yaya Toure and David Silva went close but Chelsea, defying predictions they would be defensive, soon took control of the game.
Ramires tested Joe Hart before Branislav Ivanovic lashed in a fine goal from the edge of the area.
Samuel Eto'o, Nemanja Matic and Gary Cahill all hit the woodwork as the visitors continued to dominate.
Silva did have two more late chances but City were unable to claim an equaliser.
City had been without top scorer Sergio Aguero and midfielder Fernandinho, who pulled out before the game with an unspecified muscle strain.
The Brazilian will undergo further assessment but is expected to be out for at least a fortnight.
Pellegrini said: "He has a muscle injury, we will see how long it is but it will be a couple of weeks, three or four weeks."