The five-time champions, desperate to win the trophy on home soil for the first time -- they lost out to Uruguay in 1950 in the final match in Rio and only broke their duck eight years later in Sweden -- will meet the Croatians in the June 12 opener in Sao Paulo.
But although their group does not look daunting on paper, Scolari, who led the Selecao to their last title in 2002, told reporters the favourites must not count their chickens.
"That should give us an incentive," said Scolari, who endured recent career flops at Chelsea and Palmeiras but who has galvanised the samba stars since beginning a second spell at the helm a year ago.
Asked if he had looked beyond the group phase, Scolari said no.
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"I am not concerned with the second phase," he told Brazilian television.
Brazil lost to the Mexicans in the Olympic final in London last year to leave them without the only title still missing from their collection.
"I am happy with the match sequence," added Scolari following a draw which sees Brazil start off in Sao Paulo before taking on the Mexicans in the heat of Fortaleza on June 17 and finishing with Cameroon on June 23 in Brasilia at the national stadium.
Former coach Carlos Alberto Parreira, winning coach with the Selecao in 1994 in the United States and now assisting Scolari as technical coordinator, said the World Cup had now essentially begun.
"The Cup starts when you know who you are up against. The Cup starts now," said Parreira, who dubbed the opening gambit against the Croatians as crucial.