The Dutch midfielder had several shouts for a spot-kick during the World Cup last-16 tie in Fortaleza and earned the winning penalty deep into stoppage time.
“I must apologise,” Robben told Dutch media NOS after the final whistle.
“The one at the end was a penalty, but the other one was a dive in the first half. I shouldn’t be doing that.”
The Bayern Munich man handed over the spot-kick duties to substitute Klaas Jan Huntelaar, who coolly converted from 12 yards to send the Dutch into the quarter-finals.
“Usually I am comfortable with taking a penalty, but this time I was the one tackled," said Robben. "I felt sure Huntelaar would make the most of it.
“It was his moment, he deserved this. I was almost crying from the emotions. We want to win this, to fight together as a team. I am so proud.”
Rafael Marquez, the man who was adjudged to have fouled Robben in the penalty area, disagreed with the pivotal decision.
"I believe it was not a penalty," he said. "I felt I touched the ground but I didn't touch him, maybe he touched me."
The Mexico captain said Robben, 30, who has had a brilliant career but often been accused of diving, had abused the spirit of the game.
"For 10 fouls that he receives, he lets himself fall over for five, and that's not fair play," said Marquez.
"That has to change. Unfortunately in this World Cup it wasn't just once or twice that these things affected us, but I don't want to make excuses."
- Sports & Recreation
- Klaas Jan Huntelaar