Oranje boom! Sneijder winner brings curtain down on Dunga

One of the best books written about Sir Alf Ramsey was called Winning isn't Everything and it is a phrase Dunga, in one form or another, will take to his grave. Had Brazil won the World Cup, with a team stripped of its style and with panache sacrificed to efficiency, the applause in São Paulo and Rio de Janeiro would have stopped short of an ovation.

But Brazil did not win, they were expelled from the World Cup in the grimly appropriate setting of Port Elizabeth, the centre of South African heavy industry, by the Netherlands. By the end, reduced to 10 men when Felipe Melo stamped on Arjen Robben – who had been ruthlessly targeted all afternoon – they made the kind of exit from a tournament they are expected to win by right with the kind of display Dunga's many, many critics expected.

Announcing his resignation as coach of the Selecao, Dunga admitted to bearing the heaviest responsibility for defeat. "It is sad, it is difficult," he said. "Nobody prepares to lose. If you were to look at these players' faces, you would know how they feel. The press carries on its work and the team carries on its. We did not expect this."

The pressure on any member of the Selecao is unlike that of any other team and as Dunga was quitting, elsewhere in the Nelson Mandela Stadium, Michel Bastos, who gave away the free-kick that finished with Wesley Sneijder's winner was in tears afterwards, while Robinho, who had opened the scoring in a first half the Brazilians dominated, raged about the failure to deal with "two silly balls that cost us the World Cup".

However, Brazil were beaten by other stupidities. When they were 2-1 down and in desperate need of an equaliser, Dunga removed his leading goalscorer, Luis Fabiano, for the more questionable attacking talents of Nilmar. And after opening the scoring with a long pass from Melo, which Robinho anticipated more instinctively than anyone in an orange shirt, Kaka, playing better than at any time in this tournament, forced a wonderful, one-handed save from Maarten Stekelenburg. The Dutch defence that had already lost Joris Mathijsen in the warm-up and for whom Gregory van der Wiel was having a wretched afternoon, seemed ready to crack.

The Netherlands' manager, Bert van Marwijk, considered himself lucky to be addressing a team that was only a goal down at the interval. However, by the end he wondered why Holland had not won by four or five to one.

"At half-time we said to each other that we had to improve and put pressure on the Brazilian defence," said Sneijder. "It could have been our last 45 minutes in the tournament, so we went full throttle. The feeling is fantastic, of course. If you can eliminate Brazil, one of the biggest and best teams in the World Cup, you have to savour it."

Had Brazil simply attacked the Dutch, and had they not attempted to kick Robben off the pitch, they might still be in this World Cup. There is a secret history to Brazilian football and before kick-off South African television screened it; in the form of the meeting between the then world champions and the Netherlands in the 1974 tournament. In Dortmund, Brazil, playing in blue as they did in Port Elizabeth, targeted Johan Cruyff savagely. The Dutch responded, Brazil were reduced to 10 men and exited the World Cup. The Netherlands moved on to the final.

When he was at Real Madrid, Robben was known mockingly as "El Hombre de Cristal" or the Man of Glass because of his propensity to be injured. Yesterday, he was picked out first by Dani Alves, then Melo, who was finally dismissed when driving his studs into his thigh. Holland, with their treatment of Kaka and Luis Fabiano, proved they could dish it out, too.

Under the circumstances the banner of "Give Peace a Chance" that was on display proved mockingly inappropriate. Van Marwijk remarked that if journalists looked at the video evidence they would be "ashamed for Brazilian football." The first of the "silly balls" that brought the Dutch back into the World Cup was an accident. Sneijder's cross was meant for Andre Ooijer but, although the one-time Blackburn centre-half went up for the ball, he didn't reach it. He did, however, do enough to put off Julio Cesar and the cross skimmed Melo's head and nestled in the back of the net.

Brazil seldom seemed able to recover their composure. Their captain, Lucio, might have given a penalty for handball and once more they were undone by a ball sent high into their box. This time it was delivered by Robben, flicked on by Dirk Kuyt and headed into the net by Sneijder, who ran over to the bench in a state of euphoria tapping his forehead and yelling into a nearby camera.

"It was my first headed goal," he said. "It just slipped off my bald head and went in – and I'm pretty sure it's not the sort of thing that will happen again."

Holland (4-5-1): Stekelenburg; Van Der Wiel, Heitinga, Ooijer, Van Bronckhorst; Van Bommel, De Jong, Robben, Sneijder, Kuyt; Van Persie (Huntelaar, 85).

Brazil (4-3-3): Julio Cesar; Maicon, Lucio, Juan, Bastos (Gilberto, 62); Alves, Melo, Silva; Kaka, Robinho, Fabiano (Nilmar, 77).

Referee: Y Nichimura (Japan).

Attendance: 40,186.