"There was tremendous disappointment in the locker room but I think the feeling will prevail that a draw was fair," Voeller said after Ruud van Nistelrooy struck nine minutes from time to cancel out Torsten Frings's 30th-minute free kick.
"In a way a draw is a good thing because it prevents the kind of complacency that settles in when you win clearly."
Germany went into the tournament in desperate form following a 5-1 defeat by Romania and a 2-0 home loss to Hungary.
Their performance in their Group D opener, particularly in the opening 45 minutes, was more reminiscent of their confident run to the 2002 World Cup final.
"We played very well in the first half and deserved to go into the lead," Voeller said.
"I think a draw is a fair result, though, because the Dutch did step up a gear in the second half."
Germany next face Latvia, who lost 2-1 to the Czech Republic on Tuesday, and the team will go into that game with renewed confidence.
"It was tough for both sides because we had both struggled in the warm-up to the tournament," said Michael Ballack, named man of the match after a typically bustling performance in midfield.
"I think in a way both teams rehabilitated themselves tonight," said Ballack. "We didn't know exactly where we stood but now we can be positive going into the next game.
"This is a cause for confidence. In the last month we kept losing against great teams but we proved tonight we can hold our own against a top team."
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