Kosovac started his career at Belgrade-based Crvena zvezda. In 1984 he moved to Spanish club FC Barcelona, helping them win the Cup Winners' Cup in 1984–85 and 1985–86. He moved to Swedish second-tier club IFK Kristianstad in 1986 and helped them reachpromotion to the top division in 1989–90 and 1991–92. He became player-coach for the club in 1991, remaining in that position until 1994.