Three years after they were promoted to the top flight, the Potters made it all the way to the FA Cup final last season, thrashing Bolton 5-0 in the semi-finals at Wembley before losing narrowly to Manchester City.
It was another highlight in a hugely successful era for the club under the guidance of Pulis, which has been made all the better by the hard times.
"It means everything to me and everybody connected with this football club," said the Welshman ahead of Sunday's FA Cup quarter-final against Liverpool.
"We know how important it is. We've had the disappointment.
"We went to Chelsea two years ago and ended up getting beaten there in the quarter-finals and that was difficult to take.
"Luckily last year it went for us. We had a great home tie in the quarter-finals and managed to get through, and obviously the rest is history.
"It would be lovely to go to Wembley again, it would be one of the great games and one of the great occasions for this football club."
The FA Cup exploits earned Stoke a place in the Europa League and an adventure that took in trips to Split, Kiev, Tel Aviv and Istanbul before they fell to Valencia in the last 16.
But a season that started in July and has already included 45 matches does not get any easier, with a trip to Tottenham to come in the Barclays Premier League on Wednesday before Manchester City visit the Britannia Stadium next Saturday.
Pulis said: "It's probably the hardest run we've had. They don't get tougher than that but we're in the Premier League, we're still in the FA Cup, we've been in Europe. This is something the punters could only dream about a few years ago."
Stoke's FA Cup run has been fairly low key so far, with matches against Gillingham, Derby and Crawley, but all of those have been away from home and they must travel once again to Anfield on Sunday.
Pulis said: "We haven't played one game at our place this year, all the games have been away from home so to get to the quarter-finals is a great achievement but it would be lovely to go one step further.
"There's no pressure on us. Liverpool are firm favourites, we're underdogs and I want the players to enjoy it. But if we get a result we'll be doing somersaults."
Pulis was at Anfield on Tuesday to see Liverpool beat derby rivals Everton 3-0, with captain Steven Gerrard netting a hat-trick, and the Stoke boss hailed the service given to the Reds by the England midfielder and defender Jamie Carragher.
"Gerrard and Carragher were absolutely outstanding," said Pulis. "They've been two great club players. Today, when players move around a lot, it's absolutely fantastic that you've got two stalwarts playing at Liverpool and they've been outstanding for their football club."
Stoke will be virtually at full strength, with Ricardo Fuller the only player missing as he begins a three-match ban for his red card against Chelsea last weekend.