Simunic faces the prospect of a FIFA investigation after he began chants - that reportedly have associations with Croatia's former pro-Nazi Ustashas regime - with his home fans following the 2-0 win over Iceland in Zagreb.
The 35-year-old, who was born and grew up in Australia, was recorded on video leading the chants with a microphone, which has caused a stir of controversy.
The Dinamo Zagreb captain has denied he intended to make any political statement, saying only that he associated the chant as a celebration of a country he has made 103 appearances for.
"The thought that anyone could associate me with any form of hatred or violence terrifies me," he said in a statement on Dinamo's official website.
"If anyone understood my cries differently, or negatively, I hereby want to deny they contained any political context.
"They were guided exclusively by my love for my people and homeland, not hatred and destruction."
Dinamo's statement confirmed that Simunic had used the phrase: "For the Homeland". Croatian fans replied by shouting: "Ready".
Croatia qualified for next summer's finals in Brazil despite playing for almost an hour with 10 men.
Mario Mandzukic saw red on 38 minutes, shortly after opening the scoring, but captain Darijo Srna's strike shortly after half-time was enough to seal a 2-0 aggregate win and end Iceland's hopes of reaching a first major tournament.