"I don't think we deserved for it to end like this," captain Thiago Silva said in a televised interview.
"We need to apologise to the fans, they booed us at the end, which is normal, they have feelings too. It's very tough."
Midfielder Oscar looked totally deflated after the defeat, which came just four days after Brazil were crushed 7-1 by Germany in the semi-finals.
"What can you say. We came here hoping to win third place but we didn't, it wasn't our day," Oscar said. "We lost, there's nothing to say.
"We lost a goal in two, three minutes and we were chasing the game.
"We are all very sad, the people are very sad, but we tried and we tried till the end."
Robin van Persie got the first Dutch goal from the penalty spot in the third minute, Daley Blind added a second just 13 minutes later and Georginio Wijnaldum rounded it off with a third in stoppage time.
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