"My contract with the (Serbian Football) Association expired today and I cease to be coach," the 60 year old said.
"For three years, I was looking for players that would beat Argentina, but there were no such ones here, or there were but I did not know how to find them," he told reporters after returning from Germany.
The Balkan side arrived in Germany on the back of a successful qualifying campaign but left with the worst record of any team from the group stages.
The side has now been broken up after Montenegro gained its independence last month.
Petkovic felt that injuries played a part in the team’s failure at the tournament.
The squad also faced numerous internal disputes during their brief stay in Germany.