In a statement released Wednesday on Dinamo Zagreb's website, Simunic rejected "any political context of my statement which was driven solely by my love toward my people and my country, and not by hatred and destruction."
"The thought that anyone could associate me with any form of hatred or violence terrifies me," the statement added.
The same chant coupled with the Nazi salute has often been used by Croatian fans in the past. FIFA and UEFA have often sanctioned the Croatian Football Association because of their behavior.
Two weeks ago, FIFA fined Croatia 35,000 Swiss francs ($38,000) for incidents including fans making salute gestures during its previous match in Zagreb, a 2-1 loss to Belgium on Oct. 11.
FIFA said Wednesday it was considering disciplinary action.
"We are in the process of analyzing the different match officials' reports and gathering information," FIFA said in a statement.
Simunic faces a possible suspension which could apply to matches in Brazil at the World Cup.
Croatia's former prime minister and now independent MP, Jadranka Kosor, described Simunic's act as "harmful, pitiful, illegal and unconstitutional."
Kosor added: "It is pathetic that people who perceive themselves as big patriots actually hurt Croatia the most with such chants."
At the 2006 World Cup, Simunic was the player who received three yellow cards in one match against Australia before being sent off.