The game is a repeat of the 2011 final which Roberto Mancini's side won 1-0, but in the seasons either side of that the Potters have been knocked out at the quarter-final stage.
Those defeats came at Chelsea and Liverpool, but with City set to visit the Britannia Stadium, where they have not won since 1999 when both teams were in the old Division Two, Pulis is bullish going into the tie.
"Our record is as good if not better than anyone else's in recent seasons," he said.
"You look at our record in the past three years and it is phenomenal to have only lost three games.
"Two of those were quarter-finals away to Chelsea and Liverpool and the other the final at Wembley against Man City."
Pulis insists there is no element of revenge for their final defeat of two years ago, a game he has never watched since.
"We just want to go out and do our best," he added. "We understand how difficult it will be because they are a great footballing team with wonderful world-class players.
"We need to turn up and be 110% and we need our supporters to be 110% and I have no doubt they will turn up."
Stoke's traditional defensive stability has been shaken in recent weeks, with 10 goals conceded in three league matches.
Pulis believes they have ironed out some problems in training this week but knows they cannot afford any slip-ups if they hope to extend their cup run.
And he will pick a strong side despite the fact they have a match at home to Wigan on Tuesday.
"The first goal is always key against the big teams," he added. "What we need to do is make sure we don't give silly goals away which we have been doing over the past few weeks.
"Hopefully we have got to grips with what the difference has been.
"We defend as a team and I think that is most probably where we have fallen down a bit, we have stopped doing our jobs.
"When we defend as a team we are very difficult to break down. If you defend as individuals it is much easier for the bigger clubs to score."
On his team selection he added: "Of course the game against Wigan comes into our thinking, we have to stay in the Premier League so you have to balance it off.
"But the one thing we have done at this club is treat cup games, especially the FA Cup, as seriously as we can."
While Pulis is still trying to bring players into his squad before the transfer window closes, Swansea continue to be linked with a bid for striker Kenwyne Jones.
But Pulis does not believe such speculation should be an issue for any of his players.
"They have to deal with that," he said. "They get paid exceptionally good wages to do their job and everything that surrounds it.
"Myself and the players are in the public eye all the time. You are going to be flavour of the month one minute and not the next.
"You have to handle it because it is all part and parcel of being involved in football."
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