Saturday's defeat, which featured both sets of fans throwing fireworks and a touchline brawl between rival players and staff, left 1991 European Cup winners Red Star seven points behind first division leaders Partizan.
"I came to this position in 2009 at a very difficult time for Red Star, when the club was debt-ridden and comprised only 10 players under contract," Adzic told Red Star's official website.
"I wish to take the pressure off the players and staff members so that they can prepare for the remaining two games before the winter break," said Adzic.
Red Star President Vladan Lukic said after the derby the club would hold general elections next year to inject fresh blood into its management structures.
Once a force in eastern Europe, Red Star have been reduced to playing second fiddle to Partizan in the Serbian top flight, with the champions in a commanding position to clinch a record fifth successive league title.
Red Star have not survived the winter break in European competition since 1991 and Adzic said a tight fiscal policy based on selling top players to stay afloat was the only possible course of action in the foreseeable future.
"I am quite convinced time will tell sooner rather than later that the course we pursued in the last 30 months was the only one available," he said.
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