"I'm the main responsible for the heartbreak we all share today. We take accountability for the failure during this World Cup," Martino said after Wednesday’s match against Saudi Arabia.
"My contract ended when the referee sounded the final whistle. There’s nothing more to do," he told a press conference.
Mexico was eliminated from the World Cup despite its 2-1 win over Saudi Arabia in the Group C match.
Argentina are atop Group C with six points, Poland and Mexico have each collected four points, and Saudi Arabia are at the bottom of the group with just three points.
But second-place Poland also advanced to the next stage, edging out Mexico on goal difference. Poland have a goal difference of 0 and Mexico has a goal difference of -1.
This is the first times the Mexican national team failed to qualify for the World Cup round of 16 since 1978.
Source: Anadolu Agency