Highlights - Argentina 3-1 Mexico
Mexico coach Javier Aguirre said two errors had cost his side a place in the quarter-finals after they were beaten 3-1 by Argentina in Johannesburg.
Replays showed Carlos Tevez was offside for Argentina's opener, while a mistake from Mexico's Ricardo Osorio let Gonzalo Higuain in to score the second.
"In the first few minutes we were superior but the two mistakes made a dramatic difference," said Aguirre.
Argentina will now face Germany in the last eight on Saturday.
A replay of Tevez's goal was shown on the big screen in the stadium by mistake, which led to a mass protest to the officials by Mexico's players that continued at half time.
Tevez puts Argentina into controversial lead
Mexico had only themselves to blame for Argentina's second though, as Osorio gifted possession to Higuain, who slotted home his fourth goal of the competition.
"We got disorientated by the first goal, we lacked the mental strength and concentration to overcome the error that wasn't our own, and then we committed the second one," said Aguirre.
"I told the boys, heads up, stand proud and tall, be calm and cool, everyone is human. Referees have to make spit-second decisions and they can spoil everything, it happens."
El Tri were powerless to prevent the Argentine's third goal, as Tevez rifled in an unstoppable 25-yard shot.
Higuain doubles Argentina lead
They continued to battle though and were rewarded when Javier Hernandez fired home a superb consolation.
This defeat brings to an end an inconsistent campaign for Mexico, who shone in a 2-0 group win over France but failed to match such a performance in games with Uruguay and South Africa.
"There were ups and downs, there were times against South Africa and Uruguay where we didn't concentrate like we did against France," said Aguirre.
"I am not happy and I am the one who was responsible for that, I did what I was able to do, there was something missing. Nevertheless, we can face the future with optimism.
"We have a great generation of young players who must be put to the best possible use, I believe in four years they will be at the top," added Aguirre.
Hernandez gives Mexico hope