Career
He is now a manager.
Born in Titograd, Kostić began his career playing for local side FK Budućnost Podgorica. in 1995, he would join Spanish Segunda División side Écija Balompié for two seasons. The club were relegated to the Segunda División B following the 1996-1997 season, and he returned to Budućnost Podgorica. In 1999, Kostić joined Greek Superleague side Panachaiki F.C. for six months.
He returned again to Budućnost Podgorica, where he would finish his playing career.
After his playing career ended, Kostić became a football manager. He leads Montenegrin First League side OFK Bar.