The global governing body confirmed on Monday that they had decided to suspend Simunic for 10 international matches, as well as fining him CHF30,000, after the 35-year-old made controversial chants after Croatia beat Iceland in their FIFA World Cup play-off last month.
Simunic used a microphone to address fans in Zagreb with the chant "for the homeland", to which the crowd replied "ready".
The call was used by the Ustashas, the Croatian pro-Nazi puppet regime, who ruled the state when thousands of people were killed in concentration camps during World War II.
FIFA have ruled that the veteran centre-back, who has won 105 caps for his country, must now serve a 10-match ban beginning at next year's World Cup finals in Brazil, so his international career could be over.
In response, Kovac stated he is "unpleasantly surprised, shocked and disappointed" by FIFA's sanction.
"(I am) primarily sorry for Josip, who will miss the World Cup - I (have) known him for a long time as a player and a man, and I am absolutely sure that in no way did he want to hurt anyone," the coach added.
In addition to Simunic's individual punishment, the Croatian Football Federation (NHS) has been fined CHF70,000 for the misconduct of their player.
Damir Vrbanovic, the NHS executive chairman, echoed Kovac's comments by saying he was "shocked" before adding that an appeal is "likely".
"Although we know that his (Simunic's) behaviour did not want to hurt anybody, FIFA obviously (imposed such a) draconian penalty (as it) wanted to send a strong message."
