Needing to win by two clear goals to stand any hope of progressing, Holland took an early lead through Rafael van der Vaart but were undone by goals in each half from man of the match Cristiano Ronaldo yesterday.
"We have succeeded in our great aim, which was to qualify for the quarter-finals," said Ronaldo. "Now we have to play against the Czech Republic, which is going to be hard, but we'll do our best."
From a Dutch perspective, the final score was rendered immaterial as Denmark's 2-1 loss to Germany in the other Group B match meant they would not have qualified for the last eight even in case of victory.
Portugal, for whom Ronaldo belatedly reproduced his Real Madrid form at this tournament, will compete for a semi-final place against the Czechs in Warsaw on Thursday. Runners-up at the World Cup two years ago and top scorers in qualifying, the Netherlands leave Ukraine with their tails between their legs after three consecutive defeats.
"I think we started quite well today and we scored after about 10 minutes," said Holland coach Bert van Marwijk. "But you saw that when we concede a goal, the uncertainty remains. If we'd scored a second, we might have been more sure of ourselves, but we didn't take our chances."
Mindful of the pressing need for goals, van Marwijk handed starts to both Klaas-Jan Huntelaar and van der Vaart, who replaced captain Mark van Bommel and inherited the captain's armband from him.
Van der Vaart needed less than 11 minutes to vindicate his manager's decision, collecting a pass from Arjen Robben and shaping a delightful 25-yard shot inside the left-hand post to put Holland ahead.