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GALLERY: All of the action from Day 7
France, the 1998 world champions and 2006 runners-up, were left with just a point from their first two Group A matches in South Africa and are three behind Uruguay and Mexico who meet next Tuesday.
France need to beat South Africa in their final game on the same day, and hope the mathematics work in their favour.
But the controversial Domenech, who steps down and will be replaced by Laurent Blanc after the World Cup, is not holding out too much hope of his team making the second round.
"We need a miracle now," admitted Domenech. "We have to be strong and at least play for our honour. At least we must show something in the last match. When we are forced to rely on others, there's nothing to say."
Veteran Cuauhtemoc Blanco converted a late penalty to clinch Mexico's first victory over France after substitute striker, Manchester United-bound Javier Hernandez, had put the Central Americans ahead 64 minutes into the Group A showdown at Peter Mokaba Stadium.
France, who controversially reached the World Cup finals after Thierry Henry's handball set up a decisive goal in a play-off win over Ireland, struggled to create any meaningful opportunities against a vibrant Mexican team.
"I don't have the words, it's a real disappointment for all of the people who believed in us," added Domenech.
"If we had the answers then we could have done something about it. We had good intentions and desire. I feel just like all of the fans, all the French people. It's more than just a disappointment.
"At the moment, I don't know what I will say to the players."
Chelsea star Florent Malouda admitted the players were dumbfounded by the loss.
"It's up to us to save our honour. It's a shame to lose like this. It's hard to react, but we can't go out of the World Cup without winning a match," he said.
Hernandez, 22, said victory will make the whole of his country proud.
"I am happy for so many reasons. Not just for my goal or for the man of the match award, but also because the victory brings so much joy to Mexico," said Hernandez.
"But this win is just a first step. There's a long way to go. We are not thinking yet about the match with Uruguay - we want to make the most of this for the moment."
Skipper Rafael Marquez warned Mexico they could not let the win go to their heads.
"We have to keep our feet on the ground despite this win," the Barcelona defender said.
Coach Javier Aguirre added: "It was very important to beat France - they are after all the vice-world champions. We turned in a very fine performance - but we are not yet mathematically through.
