The 65-year-old hailed his team's effort over the 90 minutes against Colombia, though he admits they could have taken a more reserved approach after scoring their second goal
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 2002 beaten finalists 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 way they performed on the night in Fortaleza.
"No one believed in us," he told reporters. "These players have skills and do this with a lot of dedication.
"We have a tough game ahead of us, but what we have foreseen, Germany was in our path to play in the final – and they know that."
Scolari admits 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 says 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. 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.
"To slow the game down a bit [is necessary] but you can't forget that for one and a half years we've been working with these players."
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 he is not all that surprised to see the Brazil faithful 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. We should consider our anthem important."