Watch Olsen's costly mistake
Denmark coach Morten Olsen refused to blame Simon Poulsen after the defender's error helped the Netherlands win their Group E opener 2-0.
Poulsen's poor header just after half-time hit the back of Daniel Agger and went in for an unfortunate own goal.
Dirk Kuyt made the game safe for the Dutch with a second in the 85th minute.
"Simon Poulsen was actually our best player. It happens to all players but you want it to happen in training not in an important game," said Olsen.
"I said to him afterwards that he had to look forward and not dwell on it as he played well."
Poulsen did save a certain goal with a superb clearance off the line following a Robin van Persie shot but the Danes were already facing defeat.
"I was just thinking, 'this can't be happening'", said Poulsen.
"Of course I take it seriously. But what can I do? I can go cry and then they can send me home. But that's not what it's about.
"You have to admit when it's your fault and today it was my mistake but I need to go forward."
The result at Soccer City means Denmark's run without a regulation-time victory over their near neighbours has stretched to a remarkable 43 years.
The Dutch have now not lost to the Danes after 90 minutes since a European Championship qualifier in 1967.
Olsen, who has been Denmark's national coach for a decade, was impressed with the Dutch performance, enhanced by man-of-the-match Wesley Sneijder in midfield, but said they have some way to go yet to lift the trophy on 11 July.
Kuyt scores second for Dutch
"The Dutch team are perhaps not the favourite, but they are an outside bet for the World Cup," he added.
"They have players like Robin van Persie, Rafael van der Vaart and Wesley Sneijder, all wonderful players, while Eljero Elia who came on and made an impact.
"It is always hard to play against a team which always keeps the ball, physically and mentally."
One bright note for Denmark fans, however, was the unexpectedly early return to fitness of striker Nicklas Bendtner.
The Arsenal player had not played since suffering a groin injury in a car accident in May, with Olsen insisting before the game that he would not be risked.
"I wasn't bluffing when I said Bendtner wasn't going to play," said Olsen.
"We had a few injuries and we had to take the risk of playing him for an hour of the game.
"He couldn't play any more but what we saw was fine and he will play again."
The Danes must now regroup for their next match against Cameroon in Pretoria on 19 June.
Match highlights - Denmark v Netherlands