The Serbian football association writes in a statement that Stojkovic chose to resign after the 0–1 loss in Leskovac.
Serbia's U21 national team captain Zoran Mirkovic will lead the A national team in Tuesday's away match against Andorra. The Serbian association announces a meeting on Friday to make a decision on the national team's organization.
Stojkovic has led Serbia for over four years and taken the national team to both the World Championship and the European Championship.
Serbia is third in the World Championship qualifying, four points behind Albania, which has one more match played, and eight points behind the dominant leader England.