The South American champions were outplayed by Brazil in a 3-0 loss in Sao Paulo on Wednesday (AEDT) to finish sixth in CONMEBOL qualifying.
Pizzi, who took charge of Chile in January 2016, said his time at the helm was over after the stunning failure.
"About the future, as I said last week, my contract ends in this situation," Pizzi said.
"It seems to me, although it is the responsibility and decision of the directors, we must speak and evaluate what they want for the team, try to choose the best option.
"Of these options, I rule myself out."
Pizzi, who led the nation to the Copa America title last year, said he was to blame for Chile's failure to reach Russia 2018.
"I am the one who has chosen the players, the systems and for all that, I reiterate that I assume responsibility," he said.