The Bayern Munich winger won a spot kick in injury time to enable Klaas-Jan Huntelaar to score the winner but admitted going to ground too easily earlier in the match.
Robben tormented the Mexican defense on numerous occasions with his pace, skill and direct running, and had several penalty appeals turned down before finally winning a spot kick in the second minute of injury time when he went down under a challenge from Rafael Marquez.
Substitute Klaas-Jan Huntelaar converted from 12 yards to send the Oranje into the last eight of the tournament, after Giovani dos Santos' opener had been canceled out by a late Wesley Sneijder equalizer.
After the match Robben insisted the incident which won the game was a justified penalty, but admitted going to ground far too easily on one occasion in the first half.
5 - Arjen Robben has won five penalties in 14 Champions League + World Cup games this season. Expert.— OptaJean (@OptaJean) June 29, 2014
"I have to be honest and must apologize," he told NOS. "One of the moments in the first half was a dive. Sometimes you get kicked, but that was not the case at that particular moment. I shouldn't have done that and I'm really upset with myself about it. It was a silly action.
"The other one in the first half was a clear penalty. If that's not a spot kick, then what is...
"The one at the end was a just penalty call as well."
Robben also revealed why he entrusted Huntelaar with the responsibility of the penalty rather than taking it himself.
"Usually I am comfortable with taking a penalty, but this time I was the one who was tackled," he explained. "I felt comfortable that Huntelaar would capitalize.
"It was his moment, he deserved this. I'm almost crying from the emotions. The feeling is so strong, we want to win this, to fight together. These youngsters ... I am so proud."