The unfancied European team took a shock lead when Marcelo scored an own goal in the 11th minute before Neymar levelled.
But Croatia, ranked 18th in the world, were holding their own in the second half until referee Yuichi Nishimura pointed to the spot after Fred backed into Croatian defender Dejean Lovren and fell.
"If anybody saw that was a penalty, let them raise their hand. I cannot raise my hand. I didn't see it," said Kovac.
Kovac branded the spot kick award "ridiculous", saying he blamed himself for not saying during Wednesday's press conference that he would be "keeping a beady eye on the referee".
The disappointed coach said he felt his team had deserved at least a point from the match, praising his players for their performance in front of passionate support for the home side.
He said he did not blame Fred for his tumble.
"I cannot blame Fred because everybody tries to do that. This is part of the sport whether you like it or not. This is part and parcel of football.
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