The South American nation failed to make it to the 2022 World Cup round of 16 despite recording a win over Saudi Arabia in their last group game at the Lusail Stadium on Wednesday night.
Mexico defeated Saudi Arabia 2-1 but agonisingly went out of the World Cup on goal difference on a night of incredible drama in Doha.
With Argentina beating Poland 2-0 in Group C at Stadium 974 and Mexico leading by the same scoreline at Lusail Stadium in the 94th minute, Gerardo Martino's side needed one more goal to prevent them from going out according to Fifa's fair play rule.
But Salem Al Dawsari's injury-time consolation goal for Saudi Arabia sent the distraught Mexicans home anyway, leaving the Polish players to celebrate across the city.
After a stop-start first half with little rhythm to it, the match burst into life two minutes after the break as Henry Martin reacted quickest to finish Cesar Montes' flick on.
Mexico fans had barely calmed their celebrations before Luis Chavez curled a glorious 30-yard free-kick into the top corner to send their supporters into pandemonium.
They thought they had another but Hirving Lozano's low strike was chalked off for offside and Martin should have had a second but volleyed over from 12 yards out.
It was all Mexico as they pushed for further goals. Chavez nearly struck another stunning free-kick but Mohammed Al Owais palmed it out, then Orbelín Pineda curled narrowly wide.
Mexico thought they had sealed progression when Uriel Antuna stroked in late on, but that too was flagged for offside and they went out in the most excruciating manner
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