Antic, who steered Serbia to next year's World Cup finals in South Africa for their first major tournament as an independent nation, said on Friday he was under no pressure to qualify for the Euro 2012 finals in Poland and Ukraine.
"We know that expectations are higher after we reached the World Cup finals but any kind of pressure to qualify for every event from now on would be completely counterproductive," Antic told Reuters.
"We have to take it one step at a time and enjoy the Christmas festivities first. We have plenty of time to prepare for the World Cup where we hope to give our fans a lot to cheer about."
Antic was named Serbia's coach of the year at a gala on Friday, while CSKA Moscow winger Milos Krasic was named player of the year.
Serbian Football Association president Tomislav Karadzic said Antic had pulled Serbia's football out of the doldrums when he took over in August 2008 only two weeks before the World Cup qualifiers started.
"We were in a deep black hole 18 months ago after failing to qualify for Euro 2008 and soccer was virtually off Serbia's sports map," Karadzic said.
Serbia were drawn in Group D with 2006 semi-finalists Germany, Australia and Ghana, who are coached by their compatriot Milovan Rajevac.
Antic acknowledged the Ghanaians would be a tough nut to crack and said: "We will soon have a chance to make an in-depth analysis of their qualities, starting with the African Nations Cup in January."
