An 85th-minute winner from Alexis Sanchez on Thursday lifted Chile into third in CONMEBOL World Cup qualifying with one game remaining.
But their final game is a trip to group winners Brazil, and they could still slip out of the qualifying spots.
Pizzi told his team they still had work to do ahead of their trip to Sao Paulo, a task made much more difficult by star midfielder Arturo Vidal's suspension, picked up due to card accumulation.
"We're going to have to keep fighting. The last effort remains and we are confident we can compete with Brazil," he said.
"We will prepare for the match in the best possible way. We still have not achieved anything and it will be very difficult."
Vidal was booked just before the hour-mark against Ecuador, ruling him out of the Brazil clash.
But Pizzi still believes in his team, who inflicted Brazil's only defeat this campaign by claiming a 2-0 win when they met in October 2015.
"It is better to be stronger, but we have already shown that in the absences of some, we have been able to impose ourselves and disguise the things we lack," he said.
"Now it will be the same. We have a team that gives guarantees."
While Peru host Colombia on the final matchday, Paraguay welcome lowly Venezuela to Asuncion and Argentina visit Ecuador.