The defeat has left Mexico in danger of missing out on next summer's World Cup finals in Brazil.
El Tri sit fourth in the final round of CONMEBOL qualifying with just one win in seven matches so far.
Luis Fernando Tena will take charge for Tuesday's difficult trip to Columbus to meet fierce rivals the United States.
"Jose Manuel de la Torre has left the coach role of the national team," a statement on the Mexico Football Federation's website read.
"The president of the Mexican Football Federation, Justino Compean, has decided to make a change in the technical department of the senior team.
"Luis Fernando Tena will be responsible of the coaching team and will be supported by the same coaches who have participated to date in this process."
A press conference was due to be held on Saturday, but Tena will have little time to turn around matters before heading to the USA.
Friday night's loss was only Mexico's second in 77 qualifying matches at Estadio Azteca and they have scored just four goals in the final qualifying round - only last-placed Jamaica have netted fewer.
Oribe Peralta opened the scoring on six minutes but Honduras struck twice in three second-half minutes through Jerry Bengtson and Carlos Costly to grab victory.
Defeat for Mexico in Ohio on Tuesday could drop them down to fifth in the standings and outside the qualifying places.
The top three teams in the CONMEBOL final round automatically book their place at Brazil with the fourth-placed team set to meet New Zealand in a two-legged play-off.
Tena led Mexico to gold at last year's Olympics and while glad to take over the senior team, he admitted he was sad to see his close friend De la Torre depart.
"Every coach wants to manage the national team, but not under these circumstances," he said at the press conference.
"They're not ideal because a friend, a boss has to go. These are not the perfect conditions because the standings are saying that we are in a very tough spot."
Tena admitted getting a result against the USA on Tuesday could be problematic.
"I have faith in these players, I know them very well and I'm sure that the team will improve," he said.
"They are committed and they are sticking together and that leads me to believe that we can play a good role in Columbus, even though nobody can guarantee a good result."