The 62-year-old coach praised his team for playing on their own terms against their Dutch counterparts and thought that all of his players reached the peak of their abilities
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Olsen described his pride at the way Denmark countered the Netherlands' early control of the match with a confident, hard-hitting style of football.
"I am very happy and proud tonight," Olsen told Danish TV2. "I think it was a fantastic performance and that we dared to play up to this Dutch team which had so many chances but we had a few ourselves too.
"Without seeing it from our point of view, we deserved to win this match. Despite the fact that we were under pressure in our own half, we still believed we could play our own game."
The Netherlands were favourites to progress from a tough Group B, in which they are joined by Denmark, Portugal and Germany. But the Danes' victory could prove to be crucial in the result of this year’s tournament.
"We know the Dutch players and if they are only really good if they can sense that their opponents are afraid of them and we didn’t allow this," Olsen continued.
"We played them the right way. The players found the solutions in the right positions and at the right times.
"There were many good performances during the whole match and that was what we said we would do at the beginning. Everybody had to peak today and I think all the players did this."