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.
"Football is like that. There are always controversial incidents. It happens to all teams. There was controversy in Spain's game, the Mexico game and our game too. And there will undoubtedly be more controversial incidents," said the 22-year-old Chelsea star in a press conference at Brazil's training base in Teresopolis.
"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."
Concern for Neymar
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.
Spain's chances of finishing top of Group B already appear slim, but if they go through as runners-up and Brazil win Group A the countries will clash in Belo Horizonte on June 28.
Oscar for one refuses to believe that Spain are out of contention yet, despite the nature of their defeat in Salvador.
"That's football. Spain had chances to kill the game but didn't do so, and Holland are a great team too," he said.
"In the second half they played really well and won. People expected more from Spain, but everyone knows they have a great team and can still qualify."
When asked if he felt the end of an era was approaching for a Spain side who have won the last three major international tournaments available to them, he added: "No, I don't believe that. Spain still have a great team and maybe such a heavy defeat will strengthen them. We must still respect Spain as the world champions."
If the sides do clash in the last 16, Brazilians are already concerned that Neymar, scorer of two goals against Croatia, might have to watch from the sidelines.
The forward picked up a booking in the opening match in Sao Paulo, so one more caution would see him forced to serve a ban, but Oscar discounted any possibility of his colleague trying to deliberately see yellow against Mexico.
Doing that would rule him out of the final group match against Cameroon in Brasilia and wipe his slate clean for the start of the knockout rounds.
"Neymar is not someone who picks up a lot of bookings so it is hard to imagine him getting another one. He is a player who usually provokes his opponents into getting booked so he will play with a clear head against Mexico."