The Dutch were beaten 4-2 in a penalty shootout against the South Americans, after their semi-final had finished goalless.
Sneijder was one of two Dutch players to miss from the spot and the Galatasaray midfielder has expressed his dislike for the way that the match was decided.
"This is hard on us. We deserved something more. Maybe we should've decided the game earlier," he told NOS. "I think there was only one team that wanted penalties and that was Argentina.
"It really does hurt. But that's football. I have to take part of the responsibility. It can sometimes go wrong. I hate shoot-outs so much."
The Netherlands will face Brazil in the third-place playoff at the Estadio Nacional in Brasilia on Saturday.