The 30-year-old was put under scrutiny after winning a decisive penalty in the Oranje's 2-1 last-16 win, particularly after he admitted he had tried to earn a free kick despite feeling no contact in the first half.
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"I can only repeat what I said after the match," the Dutchman said in an interview with the Times of India.
"I really must apologise as in the first half I took a dive and I really shouldn't do that. That was a stupid thing to do but sometimes you're expecting to be struck, then they pull their leg away at the last minute and I went to the ground without a touch.
"But I was fouled by Marquez! You can see it on television. So the one at the end was a penalty.
"Everyone is allowed to have their opinion. I said it before the game, I also say it now that I will say what I think is honest and fair. Not everyone has to agree with me, they just need to respect whatever happened.
"I am an honest guy and said what I did was wrong. That should be the end of the story. Maybe sometimes you are punished for honesty but I always prefer to be honest!"
Netherlands now face Costa Rica in their quarter-final in Salvador on Saturday and Robben admits that he regrets the fact his comments have overshadowed his side's achievements.
"It is a shame there is so much discussion because we put on a great performance as a team," he acknowledged.
"That should be the main thing. Sometimes, you know, I like to be honest and I again apologise for this action in the first half but that is football. It had nothing to do with the result of the game.
"It was a lot of hard work and some work and some luck for us in the end to turn things around so late in the game against Mexico. It was a deserving win in the end and we are proud to reach the quarter-finals.
"Costa Rica are difficult opponents, otherwise they wouldn't have ended up in a quarter-final topping a group with Uruguay, Italy and England, and then beating Greece. It won't be easy for us."