Scolari said his team showed great character after bouncing back from an early own goal and singled out 22-year-old Neymar for his man of the match performance.
"The only thing we want is that Neymar is happy playing ball. He's a special player," Scolari said after the win gave Brazil a great start in their bid for a record-extending sixth World Cup title.
Brazil fell behind after 11 minutes through Marcelo's own goal but Neymar led the comeback, scoring with a left-footed shot from outside the area and then with a controversial penalty awarded by Japanese referee Yuichi Nishimura.
Croatia's coach Niko Kovac was furious about the award of the soft 71st-minute spot kick and said the World Cup could become a "circus" if Brazil continued to get favourable calls.
Scolari, who said he agreed with the call, responded by reminding Kovac that Brazil has won the World Cup more times than any country and did it without any help from referees.
"I'm not going to comment on what my colleague (Kovac) said. The only comment I can make is that Brazil has five World Cup titles," he said. "Those weren't five circuses in favour of Brazil."
"The referee saw a penalty. It's the referee that has to decide."
Scolari, Neymar and the rest of the Brazil team are under intense pressure as local fans expect their team to deliver the country's first World Cup title on home soil.
Neymar delivered in style on Thursday, leading the comeback alongside excellent midfielder Oscar.
"He (Neymar) doesn't need all of you (the media) to demand that he become the best player in the world. His responsibility is to play for Brazil, and that's what he did today," Scolari said.
Neymar said the victory was "more than I ever dreamed or imagined. The merit belongs to the team as a whole, which remained cool and calm to come from behind and win."
Scolari also heaped praise on the Brazil supporters in the 62,103 crowd in Sao Paulo, a city with notoriously fickle fans who booed the team in their final warmup match for the World Cup.
"Our players were excellent, they showed determination to be able to come from behind. They were fantastic," Scolari said.
"But who really deserves praise are the fans. It was wonderful, the support we received here in Sao Paulo. If there's still any notion out there Sao Paulo doesn't root for the national team effusively enough, that was put to rest today."
- Sports & Recreation