The Selecao triumphed 3-1 at the Corinthians Arena in Sao Paulo but the outcome of the match hinged on the decision by Japanese referee Yuichi Nishimura to award a second-half penalty to the hosts.
With the scores level at 1-1 midway through the second half, Fred went to the ground under minimal contact from Croatia defender Dejan Lovren and Neymar converted the resulting spot-kick.
But there were some dubious decisions in Friday's matches too, with Mexico seeing two goals disallowed in their 1-0 win against Cameroon, and Oscar insisted that refereeing controversies will continue to mark this World Cup.
"The penalty on Fred might not have been that clear but there was contact and the referee, in his position, had to make a very quick decision. It was a penalty because the Croatian defender put his arm on Fred and knocked him off balance."
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While the refereeing debate goes on, Brazil are looking ahead to their second Group A game against Mexico at the Castelao Stadium in northern city Fortaleza on Tuesday, where a win will leave them on the brink of qualifying for the last 16.
However, Spain's 5-1 thumping at the hands of the Dutch has left many in Brazil contemplating the prospect of a meeting between the hosts and the reigning world champions in the last 16.