City produced a dominant display and pressured the home side throughout the 90 minutes, duly being rewarded when Zabaleta's 84th-minute strike from inside the box gave them a late win.
The Argentine defender believes his side were "fantastic" on the day and was delighted to progress to the fifth round at such an intimidating venue.
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"Today we were fantastic and very solid at the back, and up front we were very aggressive so it was a great game for us.
"The Stoke crowd push the team a lot and we knew it was going to be difficult for us. The set pieces were very solid for us today so it's great for the team."
Zabaleta also expressed his side's desire to repeat their feat of two years ago and win the trophy outright, although he did suggest that their focus remains on catching Manchester United in the Premier League for now.
He explained: "We won the cup two years ago and we know how important it is in England. We want to win the FA Cup again.
"Now that we're through to the next round we have to wait for the draw. We focus now on Tuesday, QPR away and we have to keep winning to try to catch Man United."