After coming through the youth system of Partizan, Dostanić went on to play for Timok and Rad in the Yugoslav Second League, before moving abroad to France in 1986.
After serving as an assistant to Slavoljub Muslin at Red Star Belgrade,[2] Dostanić was appointed as manager of fellow First League of FR Yugoslavia contender Obilić in November 2000.
[9] A few days after leaving OFK Beograd, Dostanić took charge of Serbian SuperLiga rivals Bežanija until the end of the season.
[14] On 23 July 2009, Dostanić was named new manager of Bulgarian champions Levski Sofia, replacing Emil Velev and signing a two-year contract.
[16] With Dostanić at the helm, Red Star Belgrade failed to win the title after three years, finishing as runners-up to arch-rivals Partizan.