Antic handed four-game touchline ban
The FSS said FIFA, the world football governing body, had punished Antic for unruly behaviour after Serbia's 2-1 defeat to Australia without specifying what the coach was guilty of.
It said FIFA also fined Antic 14,000 Swiss francs ($13,280).
"As the Serbian national team failed to advance past the group stage in the World Cup, the ban will take effect in upcoming competitive matches," the FSS said.
"The Serbian Football Association will appeal the verdict because the ban is too harsh, bearing in mind the overall sportsmanlike conduct of our entire team and staff during the World Cup.
"Effectively, it means the ban will affect Serbia's Euro 2012 qualifying campaign and it is a punishment of not only Antic, but the national team and Serbian football in general."
Serbia's Euro 2012 qualifying group includes Italy, Slovenia, Northern Ireland, Estonia and Faroe Islands.
Serbia crashed out at the group stage in the World Cup despite beating World Cup semi-finalists Germany 1-0.