With two minutes to play Mexico led 1-0 but Wesley Sneijder equalised with a fierce drive before captain Rafael Marquez was judged to have tripped Arjen Robben and Klaas Jan Huntelaar calmly scored to put the Dutch in the quarter-finals.
"It seems to me the reason (we lost) was the referee, the man with the whistle. He left us outside the next stage of the World Cup," Herrera told reporters.
"If the referee starts marking fouls that don't exist, you leave the World Cup to circumstances out of your hands. We expect the referee committee to take a look at that and that this gentleman goes home, just like us."
With victory in their grasp on a scorching afternoon at the Castelao arena, the defeat was a particularly sore one for Mexico who have reached the last 16 at six consecutive World Cups and have lost every time.
"It's a World Cup where everything was against Mexico... Out of the four matches that we had, three of them were referee disasters... Unfortunately we didn't achieve what we wanted," Herrera said.
The Mexico boss was perhaps understandably prickly about the officiating going into the game after his side had two goals harshly disallowed in their opening match against Cameroon, and a strong penalty appeal turned down against Croatia.
He said the spot kick for the Dutch could also have been avoided had Robben been booked for diving earlier in the game, suggesting the winger may not have risked going down so easily under the challenge of Marquez for the late penalty.
"He dived three times, he should have cautioned him the first time," said Herrera, who also questioned why Portugal's Proenca had been selected for the game, suggesting a referee from Africa, Asia or South America would have been fairer.
"I'm happy and calm about the performance of the boys... We'd done really well. Then the team sits back and we start to give chances to a team that had not done anything.
"(But) with the assistance of the referee they came up with this result that takes (the Netherlands) to the next stage.
"We will leave tomorrow or the day after. We hope that referee does as well."
- Sports & Recreation
- Arjen Robben
- Klaas Jan Huntelaar
- Rafael Marquez
- Wesley Sneijder