Roberto Mancini’s side had not won at Stoke since 1999 and were made to work hard for victory, creating several chances before the Argentine right-back popped up in the 84th minute to secure progression.
“It’s not by luck that Zaba gets into those positions,” Platt told reporters.
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“The way that we play we get a lot of players forward, Zaba’s been in those positions many many times and he’s tucked it away nicely as well.
“When you’ve got players of the ilk that we’ve got, they all work hard and do what they have to do but you need to sprinkle in to that mix those players that often go under the radar.
“What’s pleasing is that he scores a goal and gets some headlines, but he’s not bothered about that, those kind of players aren’t, it’s not what their playing for.
“For professionals he’s just a top man.”
The former England international insisted that his side deserved to win the tie and was delighted with the determination shown by his side to secure victory.
“Over 90 minutes it felt that we had done enough to put it to bed to be honest,” he added.
“For half an hour [of the first half] we were the only team in it, for the last quarter of an hour they got in it a little bit.
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“The pleasing thing is we’ve battled hard and defended well and kept another clean sheet, it’s pleasing from that perspective and it’s also pleasing to go through, and the goal has come eventually.”
Despite watching his side fall to their second home defeat in three games, Stoke manager Tony Pulis was full of praise for his opponents, but proud of his own side's performance in the FA Cup in recent years.
“Although we’re disappointed we’ve lost the game in the last few minutes you’ve got to give City a lot of credit,” he said.
“Their attitude today was first class.
“By playing as open as we did at times, against the best teams it gives them the chance to counter attack and create chances themselves and I thought they did that well today.
"That’s four defeats in 19 games in the FA Cup, two against Man City, one against Chelsea away from home and against Liverpool away from home so you see we’ve treated the FA Cup as an important competition and will consider to do so."
Glenn Whelan's two-footed tackle on Javi Garcia in the second half went unpunished by referee Howard Webb, although Platt and Pulis both refused to comment on the incident, claiming not to have seen the tackle.