Javier Aguirre on Wednesday resigned as Mexico coach following the team's defeat to Argentina in the last 16 of the World Cup.
The 50-year-old replaced ex-England manager Sven-Goran Eriksson in April 2009, but Sunday's 3-1 defeat to Argentina in Johannesburg was the fifth successive time the country had failed at the second round stage.
"It's very clear. The first person responsible is me. I believe that I have to resign my job," Aguirre told a news conference.
"It's the most honest solution, the fairest and it's something I have to do."
Aguirre was in his second spell as national coach having qualified Mexico to the 2002 World Cup where they were eliminated by the United States in the last 16.
He also led Mexico to the 2001 Copa America final where they lost to Colombia in Bogota.
Mexico's best performance at a World Cup was a run to the quarter-finals in 1970 and 1986 when both tournaments were staged at home.