The FIFA World Cup hosts were humiliated 7-1 by Germany in their semi-final and face the Netherlands in a third-place play-off on Saturday.
The loss to Germany led to calls for Scolari to be sacked despite the 65-year-old leading Brazil to FIFA Confederations Cup glory just last year.
But president-elect of the Brazilian Football Confederation (CBF) Marco Polo Del Nero said Scolari should stay on.
"To me, he stays," Del Nero told the Estado de Sao Paulo newspaper.
"What happened was a tactical error. That was the problem. But we all make mistakes. It can happen to anyone.
"The important thing is that he did a good job. The campaign and the preparations were good. A base exists."
Del Nero takes over from Jose Maria Marin in April 2015 and it was the first time either man had spoken since the loss to Germany.
Scolari refuses to talk about his future until after the World Cup, which finishes with the final between Germany and Argentina on Sunday.
