Now coached by colourful Miguel Herrera, who missed out on playing for Mexico at USA '94 after being dropped for punching a photographer, Mexico have in recent editions failed to live up to expectations.
In the past five tournaments the Aztecs have failed to get to the 'fifth game' and make the quarter-finals they last reached as hosts in 1986 when they bowed out 4-1 on penalties to West Germany.
After a tortuous qualifying campaign, Herrera was parachuted in for a two-legged play-off against New Zealand, which the central Americans won 9-3 on aggregate.
But despite that result, Mexico have hardly lit up the world footballing stage of late, losing their last two friendlies 1-0 to Bosnia and Portugal.
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In the latter encounter, Mexico spurned a host of chances and when they took their eye off the ball late on Bruno Alves struck the winner for Portugal in the 93rd minute.
"We haven't been that convincing when facing goal, so we have to work on it," admitted Herrera. "We have to work on keeping focus all the way to the finish. We can't be losing games in the last 30 seconds."