Scolari's side were sent crashing out of the competition on home turf this week as they were convincingly beaten 7-1 by Germany in the semi-finals.
The comprehensive nature of the scoreline ramped up the pressure on Scolari to leave his post, with Zico demanding change.
The 61-year-old, who played at three World Cups and was a key part in Brazil's iconic 1978 side, is also of the opinion that Sao Paulo coach Muricy Ramalho should take over.
"We should thank him [Scolari] and thank [assistant coach Carlos Alberto] Parreira too. But we need to choose new people with new thoughts about how to play the Brazilian way," news agency EFE quotes him as saying.
"[Ramalho] is one the greatest champions of the Brazilian league, which is one of the hardest in the world to win."
Having struggled at times in the group stage, Brazil often relied on Neymar to inspire them before the Barcelona man sustained a tournament-ending back injury in the quarter-finals.
Zico also questioned the quality of the squad at Scolari's disposal - stating many of those selected were not regular starters at club level.
"If you look at the starting players in the last year, none of them were key players at their clubs," he said.
"Look at Neymar, the best player in Brazil, but how many times was he on the bench for Barcelona last season?
"Fred, Marcelo, Hulk all played inconsistently. Even David Luiz and Oscar, you can't say they were first choices at Chelsea."
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