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 in the FA Cup 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.
And in contrast to Liverpool's league form, which has seen them struggle for goals, in their three FA Cup ties - two against lower league opposition - this season they have scored 13 times.
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.
The Dutchman does not need any reminding of the quality of the England international, whom he described as "special".
"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.
"We've missed him a bit after he went but he has done really well for all the clubs he has played for and now he's doing it again with Stoke.
"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."
Despite Stoke's obvious strengths manager Kenny Dalglish insists they cannot focus too much on what the visitors may bring to Anfield.
"We have to concentrate on our own game and worry about the opposition as and when we have to," he said.
"We know we have to compete against them."
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.
"In the cup competitions we have made changes throughout," the Scot added.
"We have used our squad and that indicates strength in depth."