Actually, Brazil hasn't played "the Brazilian way" since the mid-80's. Losing to Italy, France and Argentina sent them into rebuilding mode. Parreira got the job after Italia '90 and he instantly put Mauro Silva and Dunga, two defensive midfielders together. From then on it was all about being tight at the back and win matches with the individual talent of their forwards.
But midfielders who can create and pass have been very scarce... Kaká, Juninho Pernambucano, Juninho Paulista, Rai... not much else. They kept producing superb full-backs and attacking midfielders/strikers. But no Zicos, Socrates, Toninho Cerezos and the like. The kids that fit into that style weren't developed by their clubs or were ignored by the national team.
Nowadays it's all about 2 big, strong, athletic, tactically-aware ball-winners who then play it to the attackers. Just look at the central midfielders since '94: Dunga, Mauro Silva, Cesar Sampaio, Doriva, Gilberto Silva, Kleberson, Emerson, Vampeta, Elano, Felipe Melo, Ramires, Josue, Luiz Gustavo, Paulinho, Fernandinho. Some with more technique than others, but there's a clear pattern.