Explaining to reporters afterwards why he used a chant which had been an official salute of the WWII Ustasha movement, Simunic said he had nothing to be ashamed of because he had played for his homeland and that those who had a problem with it "could read a little and learn some history."
Simunic said he had always wanted to do that, that there was no reason for any punishment or lawsuit, and that he was not afraid of reactions by organisations such as Football Against Racism in Europe.
But in Wednesday's reaction on the website of the Dinamo football club, he said that as a Croat born and raised abroad, home to him meant love, warmth and a positive fight.
"If anyone understood my chants differently, negatively, I hereby deny any political context to my statement, which was guided solely by my love for my people and homeland, and not by hatred and destruction," Simunic said.
Minister Jovanovic told him on his Facebook page, "My dear Simunic, you need a history lesson."
The Associated Press reported that "Croatia's World Cup qualification celebrations have been marred by apparent pro-Nazi chants by fans and defender Joe Simunic."
"Video footage shows Simunic taking a microphone to the field after the match and shouting to the fans: 'For the homeland!' The fans respond: 'Ready!," AP reported, adding, "That was the war call used by Ustashas, the Croatian pro-Nazi puppet regime that ruled the state during World War II."
AP's report was carried by other media such as The Huffington Post, Britain's The Guardian, The New Zealand Herald, and Austria's Sportsfan.
Germany's Der Spiegel wrote that Simunic angered Croatian football fans by celebrating with an old Ustasha salute and fascist chant.
Serbian news agency Tanjug said he celebrated the victory over Iceland with the fans with Ustasha chants.
Zagreb police said Simunic would not be charged over the chanting because there was no crime or misdemeanor.
Zagreb's municipal prosecutor said it had asked the police to submit a report on what happened after the match to decide if a misdemeanor was committed.
The Croatian Helsinki Committee on Human Rights said Croatian laws do not ban Ustasha or communist insignia and that courts punished their use as hate speech.
The sports ministry asked the Croatian Olympic Committee and the Croatian Football Federation to urgently state what measures would be taken about the incident.