Italian defender Andrea Barzagli (left) fights for the ball with Dutch forward Robin van Persie.
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"I'm happy and proud but it is only a first step," said Dutch coach Marco van Basten, a winner of the championship in 1988 as a player.
The Italian team could only apologise and promise to lift their game.
"On behalf of my team mates, I feel I must apologise to all the fans; they, like us, did not expect this result," Italy skipper and goalkeeper Gianluigi Buffon said.