The five-time champions, desperate to win the Trophy on home soil for the first time - they lost out to Uruguay in the 1950 edition's deciding match in Rio de Janeiro and - will meet the Croatians in the opener in Sao Paulo on 12 June.
But although their pool does not look daunting on paper, Scolari, who led the Seleção to their last title in 2002, told reporters the favourites must not count their chickens.
"I am satisfied with the draw," he said. "But we shall be paying close attention to the opening phase.
Asked if he had looked beyond the group stage, Scolari responded: "I am not concerned with the second phase.
"I am happy with the match sequence," added Scolari, whose side will play Mexico second time out before their final group game against Cameroon.
Parreira wary of pressure
Carlos Alberto Parreira, Scolari's assistant, added: "The World Cup starts when you know who you are up against. It starts now.
"The opening game generates enormous pressure. Win the first match and you are well on the way to making it through.