Mexico's coach Miguel Herrera launched a furious attack on match referee Pedro Proenca for giving the injury time penalty that Jan-Klaas Huntelaar hit home to seal a 2-1 comeback victory. (Agencies)
Robben was at the centre of both incidents in the World Cup last-16 clash in Fortaleza.
"I really have to say and at the same time apologise in the first half I took a dive and I really shouldn't do that," Robben said as he celebrated the victory.
"That was a stupid, stupid thing to do, but sometimes you are expecting to be struck and then they pull their leg away at the last minute,” he added.
But the Dutch striker insisted Proenca was right to point to the penalty spot after he was challenged by Mexico's veteran captain Rafael Marquez.
"I was fouled," he said.
Mexico had been leading until the 88th minute when Wesley Sneijder scored and then Huntelaar put away the penalty.
And Herrera said referee Proenca should take no more part in the World Cup.
"The determining factor was the man with the whistle. He put us of the World Cup," he said.
"Although the first goal was down to our mistake, we had the chance to reconsider during the break before extra time, but at the end when the referee invents a penalty you go out of the World Cup,” he added.
"At the very least they can look at this and this gentleman ought to be going home like us,” said a furious Herrera.
Herrera claimed his side had been the victim of poor refereeing in three of their four games in Brazil and a European referee should never have been allocated the game in the first place.
"Out of four matches, we had three where the referee was disastrous,” he said.
"I don't understand why they had someone from the same confederation. Why not an African, Asian or South American referee? All the doubtful decisions went against Mexico,” he added.
Giovani dos Santos' strike early in the second-half appeared to have Mexico on course for their first quarter-final appearance at a World Cup on foreign soil.
Mexico's coach Miguel Herrera launched a furious attack on match referee Pedro Proenca for giving the injury time penalty that Jan-Klaas Huntelaar hit home to seal a 2-1 comeback victory.