The Croatia boss was furious at the performance of referee Yuichi Nishimura, despairing at some the decisions that the official made in favour of Brazil in the 3-1 defeat
The Selecao benefited from a penalty in the 71st minute after a foul on Fred and also saw their opponents denied an equaliser when Ivica Olic was adjuded to have fouled Julio Cesar with the score at 2-1.
The Croatia coach was incensed by what he saw as unbalanced officiating, declaring that Japanese referee Yuichi Nishimura had interpreted the match as if it was an non-contact sport.
"If that was a penalty, than we should play basketball, not football!" he fumed in a post-match interview with HTV.
"If you continue like this you will have 100 penalties. I think 2.5 billion people watching on TV saw this was not a penalty.
"This was ridiculous and if we continue in this way we will have a circus. I don't blame Fred at all. I blame the referee.
"The referee had different set of rules for us and different for Brazil. Shameful refereeing for [the] World Cup! And I am proud of my players, that is how you play for your country."
Croatia still have games against Cameroon on June 18 and Mexico on June 23, and Kovac remains confident of progressing from the group.
"With the way we played, this team has to have a place in round of 16," he continued.
"I am very optimistic ahead of the Cameroon and Mexico games."