"I spoke with him after the match and he told me that it was not a penalty," Marquez said. "He said that the first foul was a penalty and that one was not called."
Mexico has now advanced to the second round at the World Cup six straight times and not reached the quarterfinals. The last time the team made it that far was as host of the 1986 tournament.
Giovani Dos Santos gave the Mexicans the lead in the 48th minute after a goalless first half, but Sneijder equalized with a hard shot in the 88th.
It was the first time Sneijder, who scored five goals at the last World Cup in South Africa, has found the net in Brazil.
Robben, who has already scored three goals for the Dutch at this year's tournament, then earned the penalty in the fourth minute of injury time but he handed the ball to Huntelaar.
"You don't know when your chance will come, but it was today, and so you grab it with both hands," said Huntelaar, who replaced captain Robin van Persie in the 76th minute. "And it was fantastic."
For Mexico, goalkeeper Guillermo Ochoa was again the star player, pulling off two more great saves after playing a key role in holding Brazil to a 0-0 draw in Group A.
But he couldn't block Sneijder's shot and guessed wrong when diving in an attempt to stop Huntelaar's penalty.
"It isn't easy to go out this way, the way this match went," Ochoa said. "It's just very hard to deal with when victory escapes you this way."
Netherlands: Jasper Cillessen; Paul Verhaegh (Memphis Depay, 56th), Daley Blind, Ron Vlaar, Stefan de Vrij, Dirk Kuyt; Nigel de Jong (Bruno Martins Indi, 9th), Georginio Wijnaldum, Wesley Sneijder; Arjen Robben, Robin van Persie (Klaas-Jan Huntelaar, 76th).
Mexico: Guillermo Ochoa; Francisco Rodriguez, Rafael Marquez, Hector Moreno (Diego Reyes, 46th), Miguel Layun, Paul Aguilar; Carlos Salcido, Andres Guardado, Hector Herrera; Giovani Dos Santos (Javier Aquino, 61st), Oribe Peralta (Javier Hernandez, 75th).