It was always going to be a struggle for Croatia to overcome Brazil, who were cheered on by a raucous crowd in Sao Paulo. However, his side looked like spoiling the party, as Marcelo diverted a cross into his own net and Croatia led after just 11 minutes.
Yet a brace from Neymar - including a hotly disputed penalty - and a late goal from Oscar on the counter attack sealed a 3-1 win for Brazil, but there were plenty of contentious decisions and they all seemed to go in Brazil's favour, prompting many to suggest that the home side were being favoured.
Manager Kovac did touch on the award of the penalty, but can be equally frustrated at seeing Ivan Perisic's goal - which would've tied the game up at 2-2 - ruled out for unknown reasons. The 42-year-old is taking charge of his first World Cup campaign as a manager, but said that his side should go home if that's how the game is going to be refereed.
"If that's how we start the World Cup, we 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. It's a shame," he added.
Croatia were unlucky in defeat against a shaky Brazil side, and there can still be cause for optimism. They head to Manaus on Wednesday to take on Cameroon, in a game that they will be looking to win having given Brazil a real test tonight.
However, Kovac's points about the refereeing will no doubt make the headlines after a number of controversial decisions went in Brazil's favour. We've seen allegations of favouring the home side before, particularly in 2002 with South Korea, and he last thing FIFA will want is further accusations of tampering amidst all the fallout from the Qatar World Cup bid.