The Selecao took the lead through David Luiz but were pegged back by Alexis Sanchez and forced to a 1-1 draw after 120 minutes.
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Julio Cesar pulled off two shootout saves - while David Luiz, Marcelo and Neymar converted their spot kicks as Brazil overcame huge pressure in Belo Horizonte to reach the last eight of the tournament, and Scolari admitted that the profligacy and "politeness" almost cost the team.
"We scored the goal, then we suffered a goal from a throw in, which is unacceptable in modern football," head coach Felipao told reporters. "After that, we had three or four chances to score a winner and we couldn't do it because of lack of precision. That's when we always get under more pressure. The possession was the same, but we couldn't score.
"We had a discussion in the dressing room, after the game, about how we're being too nice and too cordial with our opponents. It's time we show that we can't be laid back every day. It's time we defended a little differently, to go back to my style which is slightly more aggressive. I can't stand all this politeness any more."
World Cup host Brazil handled the immense pressure in the shootout brilliantly and the trainer - who lifted the trophy with the Selecao in 2002 - conceded that the fanatical support in the nation has its drawbacks.
"We felt really tense," he said. "It's not easy to play a World Cup at home.
"We could just admit that reaching the final is hard enough, but the team and the fans have embraced the idea of us being champions. And we will be. We could dodge the subject. But confidence is what the people are expecting and we must maintain that."
Scolari's men will face Colombia in the last eight of the World Cup after James Rodriguez's two goals saw the team past Uruguay shortly after Brazil knocked out Chile.