Zabaleta burst forward to score the game's only goal in the closing stages, earning City a place in the fourth round with a hard-fought victory.
The Argentine full-back has now struck three times this season and has called on his side to take their performance at the Britannia into their next league match.
He told ITV Sport: "Three goals this season is not bad for a full-back but it's a massive win on a tough pitch and it's difficult to win here.
"Today we were solid at the back, and up front we were very aggressive. The Stoke crowd push the team a lot and we knew it was going to be difficult for us.
"We want to win the FA Cup again but we must now focus on Tuesday and catching Manchester United."
Roberto Mancini's men return to league action on Tuesday night with a trip to Queens Park Rangers.