"We had a horrible match. About my decision (whether to resign), the fact is I'm trying to digest this defeat and think calmly what to do," a shell-shocked Osorio told reporters.
"What happened today was shameful, a football accident, it was a very poor performance and I offer my apologies to everyone and all the Mexico fans," said the Colombian, appointed in October to steer Mexico to the 2018 World Cup finals in Russia.
"I got it all wrong, I erred in my choices for the squad, I assume that responsibility, none of our players were at their best."
Osorio said there was not such a gulf between Mexican and Chilean football despite the South Americans' domination throughout the game.
"I didn't imagine such a big defeat and, with all due respect to Chile, there isn't a seven-goal difference between Chilean and Mexican football," he said.
"I have no explanation for the defeat, the third goal killed off all our possibilities. I see a very powerful Chile team with good chances of winning the competition."
Veteran defender Rafael Marquez put his faith in the work Osorio has done in charge of the team.
"Today (we have to) keep cool heads, think things through properly... and see that this simple result mustn't affect what we've been doing with professor Osorio, so I would give him the vote of confidence to carry on with this job," he told La Aficion (www.laaficion.milenio.com).
Chile won the 100-year-old competition for the first time with a victory on penalties in the final of the 2015 tournament they hosted.
Mexico, previously a guest side from the CONCACAF region in the South American tournament, have reached the final twice but never won it.
Chile meet Colombia in the second semi-final on Wednesday with favourites Argentina, looking for a 15th title, facing the United States in the first on Tuesday.
(Reporting by Carlos Calvo in Mexico City, writing by Rex Gowar, editing by Sudipto Ganguly)
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