The Netherlands midfielder missed a penalty in a 4-2 shoot-out defeat and accused the South Americans of a lack of ambition during the game
Neither side could break the deadlock over 120 minutes of action, with Arjen Robben denied by a last-ditch tackle from Javier Mascherano, before Rodrigo Palacio and Maxi Rodriguez went close for the Albiceleste.
That mean the lottery of a penalty shoot-out, where Sergio Romero saved from Sneijder and defender Ron Vlaar for Argentina to clinch a place in the World Cup final, much to the dismay of the Galatasaray midfielder.
"We deserved more," the 30-year-old insisted.
"Argentina gambled on deciding the game on penalties, while we always tried to win. I missed my penalty, I am sorry, but we could also have scored one of our opportunities in the 120 minutes."
Dirk Kuyt was in similarly despondent mood after the game and in no mood to congratulate Argentina on their victory, claiming he was not impressed with Alejandro Sabella's side.
"Argentina have not impressed, despite having players the calibre of [Lionel] Messi," he added.
"We have expressed a great defensive game, but we did struggle to find [Arjen] Robben and [Robin] Van Persie.
"I'm disappointed, we came so close to reaching a second successive final."
Netherlands face Brazil in the third place play-off on Saturday as they bid to round off the competition on a high note.