Robben dived theatrically, and not for the first time in his career, after Mexico captain Rafael Marquez challenged him in the dying minutes of their match at the Castelao arena.
His comments came after he admitted he dived in the first half provoking the Dutch FA (KNVB) to issue a statement earlier on Monday seeking to clarify the media interpretation of the player's quotes on Dutch TV after the match.
Robben later told a packed media conference at the Netherlands training camp at the home of Rio club Flamengo: "I tried to explain what happened, but sometimes you are punished for your honesty.
"After the game I was trying to be honest about what happened. I said that in the first half I went to ground without being fouled, without being touched and that was a stupid action from me.
"I think we should have had another penalty in the first half anyway, but in the second half it was a clear penalty, a clear foul. There should be no discussion about that."
Asked if he thought he might be sanctioned by FIFA for his honesty, he laughed off the suggestion saying, "I am an honest guy, I am a straight guy, that's my personality and I apologise for what happened in the first half."
Earlier, Delia Fischer, FIFA's spokeswoman, said she was unaware of any likely punishment for the 30-year-old Dutch winger, one of the outstanding players in the tournament.
"We ask players to play in the spirit of fair play," she said. "It is up to the referees to manage the match in all areas and they are trained to identify simulations and issue cards to discourage this behaviour."
Several media reports had erroneously reported that Robben admitted diving for the penalty that led to the victory.
In the news release, Robben was quoted as saying the decision to award a penalty at the end of the game, when he went down under Marquez's challenge, was the correct one.
Klaas-Jan Huntelaar scored the penalty to give the Dutch a dramatic victory minutes after Wesley Sneijder had equalised with a ferocious thunderbolt of a shot.
In the television interview, Robben also claimed he should have been given two other penalties before halftime.
"He tackled me on the shin and then had to go off himself with injury," Robben said of Hector Moreno, who suffered a suspected broken leg in the incident.
"I was tackled again and if that wasn't a penalty, then I don't know what is," Robben told NOS.
Angry Mexico coach Miguel Herrera accused Robben of diving three times and said he should have been sent off.
"If the referee was fair, their second goal wouldn't exist because Arjen Robben would have been sent off for a second yellow card," he said of Portuguese official Pedro Proenca.
"But if you don't book him after the first one, then the player knows he can get away with it," he told the post-match news conference after Sunday's game.
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