The former America boss was furious that Portuguese referee Pedro Proenca failed to caution Arjen Robben for diving and then awarded the winger a decisive late penalty
"Today it was the man with the whistle who eliminated us from the World Cup," Herrera said.
"If a referee invents a penalty, you're out of the World Cup," Herrera added. "I hope they have a look at what happened and that this gentleman goes home just like we are."
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El Tri led through a long-range Giovani dos Santos strike but Wesley Sneijder brought the Dutch level two minutes from the end of normal time. In the second minute of injury time, referee Pedro Proenca pointed to the spot after Arjen Robben was deemed to have been taken down by Rafael Marquez.
Substitute Klaas-Jan Huntelaar converted the penalty, and after the match Herrera was furious that Robben had been awarded the decision, claiming the Bayern Munich man had been diving throughout the match without punishment.
"[Robben] dived three times, and the referee should have booked him the first time," Herrera said. "The referee should go back and caution the guy who tried to cheat. If that’s the case Robben doesn’t do it the second time."