Mihajlovic vowed to qualify for next year's finals in Brazil when he took over last May but having collected only seven points from the opening six games in Group A, nine less than leaders Belgium and Croatia, the 44-year old acknowledged Serbia had only a theoretical chance of advancing.
"Mathematically we are still in the hunt and no matter what happens we want to win every game until the end of the qualifiers, but if we fail I will step down as I promised when I took over," the former international defender told daily Vecernje Novosti.
"Perhaps I put the bar too high and it would have been much easier to go along with the football federation's objective of merely injecting fresh blood into the team for the future.
"I am glad they have full confidence in my project of building a team capable of doing well but the fans and the media don't seem to be on the same page and I also miss daily work in a club because sitting at home for two months between games is not my cup of tea," he said.
Mihajlovic won the European Cup with Red Star Belgrade in 1991 before he moved to Italy's Serie A, where he played for Roma, Sampdoria, Lazio and Inter Milan and then coached Bologna, Catania and Fiorentina.
He made a reasonably good start in the qualifiers with a 0-0 draw at Scotland and a 6-1 home drubbing of Wales but three successive defeats, 3-0 at home to Belgium, 1-0 in Macedonia and 2-0 at bitter Balkan rivals Croatia derailed Serbia's campaign.
Last week's 2-0 home win against Scotland did little to lift the gloom or boost Serbia's hopes of reaching next year's tournament after Belgium beat Macedonia 1-0 and Croatia won 2-1 in Wales to effectively whittle the group down to a two-team race.
Heavily criticised for making wholesale changes to the team for every match, Mihajlovic defended his decision by stressing that Serbia did not have enough depth in the squad.
"The back four and (striker) Filip Djuricic are the only automatic starters because we don't really have adequate cover for them but all the other spots in the first eleven are up for grabs," he said.
"I will sit down and talk to the FSS when my contract expires in October and I must thank them for providing the perfect facilities and working conditions, but as things stand it is unlikely I will change my mind and carry on if we don't qualify."