Relegation battlers Palace secured a famous victory over Antonio Conte's men at Stamford Bridge, which saw Sam Allardyce's side come from behind to beat the Blues 2-1.
With Tottenham - who sit second in the Premier League standings - beating Burnley 2-0 on Saturday, Chelsea's lead at the top of the standings has been cut to seven points.
Fourth-placed City, meanwhile, take on Arsenal at the Emirates Stadium on Sunday before following up that game with a trip to Stamford Bridge on Wednesday night.
And despite Chelsea's loss to Palace being only the Blues' fourth of the season, Cahill admits it has increased the pressure on the team to ensure they secure a win over City next week - although he fully expects the players to respond with a victory.
"We're disappointed as we had a chance to chalk another three points off," the defender told BBC's Match of the Day.
"They made it difficult. It was a crazy 15 minutes once we settled it was one-way traffic.
"I hate possession stats. It's about putting the ball in the net. We have to regroup. It's a little set back but we need to focus
on Wednesday. We need to keep calm and go again.
"The gap is still there. It puts emphasis on Wednesday. It adds a bit more pressure but the boys respond to that."