He is best known for his spell with Red Star Belgrade in the 1980s and 1990s, being part of the side's European Cup victory in 1991.

Stošić played in the last edition of the Yugoslavian League before he left for Spain in January 1992, where he proceeded to be an undisputed starter for both RCD Mallorca and Real Betis, although he was relegated in his debut season with the former.

After failing to feature in the first half of 1996–97 with the latter, he moved to Mexico with Atlante FC, where he teamed up with former Red Star teammate Miodrag Belodedici; he closed out his career the ensuing summer at the age of 33, with Portugal's Vitória de Setúbal.

[1][2] He was relieved of his duties on 22 December 2013, shortly after manager Pepe Mel, due to poor results.

[3] On 12 September 1990, Stošić earned his sole cap for Yugoslavia, in Belfast against Northern Ireland: it consisted of one minute, as he came on as a substitute for Dragan Stojković in a 2–0 win for the UEFA Euro 1992 qualifiers, with the nation winning its group but not being allowed to participate.