Netherlands were run ragged by a magical performance from Russia playmaker Andrei Arshavin, who set up the crucial second goal in extra time and then got his name on the scoresheet four minutes from the end.
Van Basten believes the Dutch were simply outplayed by Arshavin and striker Roman Pavlyuchenko.
"We had a lot of problems with the attackers Pavlyuchenko and Arshavin throughout the game," added Van Basten, who scored the second goal for Netherlands in their 2-0 win over USSR in the final of Euro 1988.
"That really is the reason we couldn't come into the game."
The game also marked the end of goalkeeper Edwin van der Sar's Netherlands career, with the Manchester United stopper retiring from international football.
The 37-year-old is their record cap holder with 128 and he made his debut in 1995 under then coach Guus Hiddink - who is now in charge of Russia.
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Van der Sar admits Russia deserved win
Van der Sar, who also equalled France defender Lilian Thuram's record of 16 appearances in European Championship finals, said: "We were not good enough to beat this Russian side.
"One has to admit it, they played fantastically well. It is really a pity to leave the tournament in this way after having started so brilliantly.
"Now, we have to confront the future. But it will be without me. This evening, one shouldn't criticise anybody, it isn't the time to point fingers at anybody."