After seeing Greece win the 2004 tournament with a negative brand of football, it looked as though the Dutch were going to do the opposite four years on.
They produced an attacking masterclass in the group stages, netting a total of nine goals in wins over Italy, France and Romania, and were immediately tagged as favourites to go all the way.
But they came unstuck at the hands of Russia, who beat Holland at their own game in grabbing a 3-1 extra-time success in an open quarter-final in Basle on Saturday night.
The Dutch may have bowed out of tournament but they can do so with their heads held high, according to Van der Sar.
And the Manchester United goalkeeper believes his side, the Russians and a number of other countries have played the game how it should be played this month.
"Hopefully we will see more games like this," said the 37-year-old, who equalled the record held by Lilian Thuram in playing his 17th match in European Championships in the end-to-end contest at St Jakob-Park.
"We don't like to see teams play defensively, when even if you are behind you play with nine men behind the ball.
"This is the start and hopefully we will see some changes.
"I think they (Russia) have taken some of their game from Holland and the way Russia played against Sweden is the way forward."
It comes as no surprise that Russia - known down the years for being a disciplined and technical team but one lacking in flair - have only really changed their style since Dutchman Guus Hiddink became their coach in 2006.
And the 61-year-old was the architect behind Russia's qualification to the last four, his thorough knowledge of the Dutch squad and their way of playing enabling Russia to outsmart Marco van Basten's team against all the odds.
The results were spectacular, Roman Pavlyuchenko putting the Russians deservedly in front and they should have had the match sewn up before Ruud van Nistelrooy took it to extra time with a stooping header from an 86th-minute Wesley Sneijder free-kick.
But Hiddink's energetic side were not to be undone and in an added 30 minutes that they completely dominated, Dmitri Torbinski and Andrei Arshavin scored late goals to send the team through to a semi-final against either Italy or Spain.
Van der Sar, who retired from international football after Saturday's match, admitted the Hiddin factor swung things Russia's way.
"He knows a lot about his own team, but he knows a lot about our team as well," he said of Hiddink, who coached Holland between 1995 and 1998 and gave Van der Sar his international debut.
"It is quite good to be able to prepare your team when you know the team you are playing as well as your own. Of course it helps.
"But we didn't really start the game well and that made it hard for us."
Van der Sar added: "They have got a great chance now. They have everything - speed, good passing, great players.
"Obviously they are one of four but they have a great chance."
A lot will be made of Russia's superior fitness in the latter stages, even though they played a tough game against Sweden just three days earlier while Holland had been able to rest all their key players for their last pool match.
"That's a question for me," said Van Basten. "Normally we (should be) more in shape than the Russians but we didn't see that, which was a pity."
Van Basten leaves the international scene to take up the coaching post at Ajax and his managerial future looks bright too.
But he admitted it was disappointing to go out on such a low ebb, saying: "In the pool stages, we played well and we wanted to do that again, but from the first minute (against Russia) we weren't really in the game.
"We weren't playing football, we weren't part of the game. It's amazing we were able to keep it goalless until the second half."
Midfielder Orlando Engelaar added: "I don't know exactly what the explanation is.
"It is a shock that we are out of the tournament, I don't know what went wrong."
Mario Melchiot, the Wigan right-back, believes it was all to do with the Midas touch owned by Hiddink.
"He knows everything - he knows our players, he knows how we play," he said.
"Tactically, he is in a different class."
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