City began 2013 with a routine 3-0 win over Stoke at the Etihad Stadium but they remain seven points off the pace set by their rivals at the top of the table.
City lost ground as they were beaten in the Manchester derby just over three weeks ago and then suffered a shock loss at Sunderland on Boxing Day.
Zabaleta feels they have responded well to those setbacks but they must keep working hard.
The Argentina defender, who opened the scoring against the Potters, said: "The most important thing is always the performance of the team.
"We played a great game, we had a lot of chances, defensively we were very solid and it's another clean sheet.
"It's a good three points to carry on and we know that we are under pressure because we need to win every game.
"We know we are seven points behind United so it's going to be very tough, but keeping positive and keeping working is the key to catching United.
"It was hard to lose against Sunderland but always you need to try to respond well. We did it and I'm very proud for the team."