The Blues' stand-in skipper believes David Moyes' side will be looking for an immediate response following their FA Cup defeat at the hands of Wigan on Sunday.
The 28-year-old told the club's website: "Everton away is always very tough. It's a game that they always want to win and it is going to be hard for us. They will be hungry too, after they lost to Wigan last weekend.
"But we are aware that we need to get three points and keep winning games for our own reasons, so we know what we have to do before we leave for the international break."
Despite their disappointing FA Cup exit, the Toffees have only lost once on home turf this season and Zabaleta says the Blues must hit the ground running in order to get a win at Goodison.
He added: "Defensively we have to be very organised and fight for every ball and with the quality we have we need to create and take our chances when they come along."
Zabaleta admits that City can't afford any more slip ups if they are to catch rivals Manchester United, who are 12 points clear at the top of the Premier League table with only 10 games remaining.
The defender continued: "We're under pressure now because we need to win every game - if we drop points it is just not good enough anymore - but we just have to keep working hard and believe."
After the Merseyside encounter, Zabaleta will return home to represent Argentina in their World Cup qualifying campaign.