With the Potters well on their way to securing a fifth successive season in the Barclays Premier League most top flight sides have become well accustomed to their style.
But when Kuyt initially came up against them is was something of a shock.
"I was not used to playing against these types of teams in Holland," said the World Cup runner-up.
"I've never played against another team in Europe who play like that.
"They've got a good team and physically they're one of the strongest teams in the league.
"But they're doing well, they're getting results and if you see what they have achieved over the last couple of years, it's impressive."
Familiarity with Stoke's methods will not be a problem on Sunday in the quarter-final at Anfield as it will be the fourth meeting of the season.
The Potters are ahead on results in the current campaign, having won in the league at the Britannia and left Anfield with a goalless draw in January, although Liverpool did beat them in Staffordshire on the way to their Carling Cup triumph.
Overall the Reds' record is much better against Stoke. In six FA Cup meetings, which includes two replays, the Potters have never won or even scored.
The Potters have also not had a victory at Anfield since 1959, a run of 32 matches without success.
But Kuyt is wary of how difficult Tony Pulis' side can make things for opponents and they will not be underestimated.
"It's always tough against Stoke. You know what it's about and we know what Stoke City are about," he told liverpoolfc.tv.
"The Premier League is about the physical game. There is a lot of quality but physically it's also one of the toughest leagues."
Kuyt will come face to face with former team-mate Peter Crouch again with the tall striker after he was rested for last weekend's match at Chelsea despite scoring twice in three matches.
"It was great to play with him. He was a great player here, he scored some great goals, and he was also a great lad in the dressing room and outside the training ground," said the 31-year-old.
"He is very strong in the air but, especially when he was here, he was very good with his feet as well. Peter is a special player."
Dalglish has injury concerns over Craig Bellamy and Glen Johnson with the former more likely to return after missing the midweek Merseyside derby victory.
He will consider making changes to his side, however, with a league match at QPR on Wednesday to consider as well but that will not mean he will put out a weakened team.
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.
"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."
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 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.