Fred went down in the 69th minute of the Group A match on Thursday with the score 1-1. Japanese referee Yuichi Nishimura immediately pointed to the spot, incensing the Croatian players, and Neymar converted the kick.
"It was a clear penalty, there's no such thing as a more penalty or a less penalty," Fred told the Brazilian Football Confederation's TV channel on Friday.
"I controlled the ball and was about to turn, I got a hit on my shoulder, I lost control of the ball, I lost my balance and I fell," he added. "I am not a player who throws himself to the ground.
"I see lots of people saying it wasn't a penalty but there was contact and it was enough to knock me off the ball and stop me scoring.
His comments came just moments after FIFA's head of refereeing defended the experienced Japanese official.
Massimo Busacca, in charge of refereeing for world soccer's ruling body, told reporters in Rio De Janeiro that Nishimura's decision appeared to be justified.
"The referee was in a very good position," he said of the 42-year-old match official.
Busacca said a photograph of the incident showed there was contact between the two players in the penalty box, and that Dejan Lovren touched Fred not only with his left hand but also his right.
"If you make contact you permit the referee to go in one direction," he added.
Busacca declined so say whether Nishimura would officiate at other matches during the World Cup, as he and his team had yet to make a full analysis of the referee's performance over the full duration of the opening game.
When one reporter suggested that Nishimura's decision was a mistake, Busacca replied: "A mistake It's your opinion and I'll let you think it if you want."
Croatian manager Niko Kovac was furious with the award and hit out at officials.
"If that's how we start the World Cup, we'd better give it up now and go home," Kovac said.
"We talk about respect, that wasn't respect, Croatia didn't get any. If that's a penalty, we don't need to play football anymore. Let's play basketball instead."
Nishimura showed Felipe Melo a red card as Brazil crashed out of the World Cup quarter-finals in 2010, effectively ending Brazil's hopes of coming back from 2-1 down and their dreams of a sixth world title.
Fierce debate over refereeing decisions was unlikely to end with Nishimura's intervention.
One of the main talking points after Friday's game between Mexico and Cameroon at a rain-soaked Dunas arena in Natal was the officiating, after two Giovani dos Santos efforts were controversially disallowed in the first half.
Mexico went on to win 1-0, however, thanks to a Oribe Peralta goal.
FIFA is using goal-line technology for the first time at this World Cup, and FIFA president Sepp Blatter this week suggested introducing a television referral system allowing managers to challenge up to two refereeing decisions per match.