Saturday's loss was their first in a home qualifier since 2001 and saw them lose ground on the automatic qualifying spots.
Mexico sit two points behind third-placed Honduras with three games to go, and currently occupy a position that would only be good enough for an intercontinental play-off place.
Their recent performances in qualifying matches - they had won one of their previous six, drawing the other five - had brought criticism of the manager and their first defeat of the campaign saw him lose his job after two years at the helm.
Oribe Peralta opened the scoring in the fifth minute against Honduras but goals from Jerry Bengtson and Carlos Costly saw the visitors leapfrog Mexico in the group.
A statement on the Mexican Football Association's website confirmed that the 47-year-old had been relieved of his duties.
De la Torre had been in charge of the national side since 2011, including reaching the Round of 16 in the 2010 World Cup.
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