The Blues have won just one of their six away league games and missed the chance to move into third spot after going down to a 1-0 defeat at Sunderland on Sunday.
However, despite their poor start to the campaign, Manuel Pellegrini's men remain six points off top of the table Arsenal in eighth position.
But City's player of the year last term Zabaleta says the club must start keeping clean sheets if they want to compete for the title.
"I don't know if it is just about our away form - when you look at the games we have played away, we have dominated all of them," said the 28-year-old Argentine right-back.
"But it is true we cannot keep a clean sheet, and when you play away you must defend much better, and try not to concede goals. It's not happening, every time we play away.
"There is a long way to go and we have too many games to the end, but when you lose points like that it will be really difficult to fight for the title."