The hosts' excruciatingly tense 3-2 penalty win, after the game in Belo Horizonte ended 1-1 following extra-time, left them three games away from lifting the World Cup for a sixth time and exorcising the ghosts of defeat in the 1950 final on home soil.
"We took upon ourselves this mission that we must be champions. If you make a promise you must deliver. This is what the players are doing," Scolari told reporters.
"There are three more (games) to see if we can reach heaven," he added.
"The World Cup has show that teams are very balanced. If you cannot exploit one or two or three chances, as we didn't today, then you might pay the price for that and go out."
Asked about tension between the Brazil and Chile benches during the game, Scolari warned he may abandon a new-found patience and revert to a more explosive style.
At times, the fourth official had to restrain Chile's bench, with assistants to their coach Jorge Sampaoli straying beyond their area and gesticulating aggressively.
"We are being very cordial, very nice and polite to the foreign teams. But perhaps it's time for us to change," he said, alleging someone threw stones at Brazil's dugout.
"They were almost encroaching into our area. It was almost like war, they were waging a battle. I can't hold it in, I can't be polite any more."
Scolari was critical of the mix-up at the back between Hulk and Marcelo that led to Chile's equaliser by Alexis Sanchez in the first half that cancelled out David Luiz's early strike, saying it was unacceptable at international level.
But he piled the praise on his leading forward Neymar.
The 22-year-old striker had a quiet game by his standards but coolly converted his penalty in the shootout.
"He's mature. He has been ready since he was 17 or 18 years old. He is a simple player, he likes playing football. He takes a penalty as if he was playing with friends," Scolari said, adding that Neymar took a kick on the thigh and will take a few days to recover.
"We will do our best to have him on the pitch for the next match," added Scolari.
- Sports & Recreation