A battling 2-1 win over Jose Pekerman's side sealed the Selecao's spot in the last four on Friday, where they will face Germany, who overcame France.
Scolari was furious with Brazilian media in the build-up to the last-eight encounter following criticism of his side's displays so far and was thrilled with the performance on the night in Fortaleza.
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"We have a tough game ahead of us but what we have foreseen [was that] Germany was in our path to play in the final – and they know that."
Scolari admits that his side could have allowed themselves to take their foot off the accelerator when David Luiz struck the second goal of the night, though he has come to expect the same high-intensity work-rate from his charges.
"I'm going to look at our players and expect them to recover," he continued. "The rhythm in the second half when we scored and we went 2-0 up and we could have slowed the game down, we accelerated ... we don't need to do that. We don't need a player who stops the ball because he might not run. My team runs a lot.
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Brazil got off to a fantastic start when Thiago Silva scored in the first seven minutes following another awe-inspiring rendition of the national anthem but Scolari says that he is not all that surprised to see fans so vociferous in their support.
"For many years Brazil has been trying to embed in children that they have to respect their anthem and, when we see how the crowd reacted – the crowd in Fortaleza was excellent again – we have to say that it is important," he argued. "We should consider our anthem important."