Scolari’s side had to come back from a goal down after Marcelo put through his own net to triumph 3-1 in front of an expectant nation and a packed stadium in Sao Paulo, with Neymar scoring twice and Oscar adding a late third.
There was a huge degree of controversy over Neymar’s second goal, which came from the penalty spot as Japanese referee Yuichi Nishimura ruled that Fred’s tumble to the floor following the slightest contact from Croatia defender Dejan Lovren warranted a penalty.
The European side were incensed, surrounding the referee and protesting vehemently, before Neymar stepped up to beat Stipe Pletikosa to give his side a 2-1 lead in the 71st minute, although the goalkeeper got both hands to the ball.
Scolari said: "Thousands didn't see the penalty? The referee saw it and he is the one that decides. We also think it was a penalty.
"I watched it 10 times and, for me, it was a penalty."
Brazil were far from convincing as they embarked on a quest for their sixth World Cup triumph, with goalkeeper Julio Cesar forced into action on several occasions.
But Scolari had no intention of publicly criticising his squad as he told Fox Sports Brasil: "I'll tell the players first what I didn't like, not you."
The Brazil boss did, however, have words of praise for Chelsea playmaker Oscar, who was excellent throughout, and also backed Croatia to progress to the next phase.
He said: "He (Oscar) is this player we all know, I had no doubts. He is wonderful, excellent.
"If I could bet who will advance in this group, I would bet on Croatia."
Brazil’s hero Neymar was involved in another controversial incident in the first half when his elbow caught Luka Modric in the throat, with the Barcelona man booked for his clash with the Real Madrid midfielder.
But Neymar was quick to play down the incident after the game and insisted there was no intent in the collision.
He said: "It's complicated when you get a yellow card in the first match. My elbow hit Modric's face and I actually wanted to apologise as I didn't see it happening.
“If the referee saw mischief, he could have given a card, but there was no mischief at all."
And David Luiz told Globo: "The score doesn't show how the game was. Croatia are a good, smart team. This is the first step. we have six more steps. We know the other games won't be easy."