Playing Career Zagorac primarily played as a defender. His professional career began before the establishment of FK Sarajevo, playing for local teams. He joined FK Sarajevo shortly after its founding in 1946 (then named SD Torpedo) and quickly became a cornerstone of the team. He served as captain and was instrumental in the club's rise from the lower divisions to the Yugoslav First League. He played for FK Sarajevo from 1947 to 1955, accumulating 298 official appearances for the club. He was known for his strong defensive presence and leadership qualities on the field.
Managerial Career After retiring as a player, Zagorac transitioned into coaching. He returned to FK Sarajevo on several occasions to manage the team. His most notable achievement as a manager came during his second stint with FK Sarajevo, when he led the club to its first-ever Yugoslav First League championship title in the 1966–67 season. This historic triumph cemented his legacy within the club.
Beyond FK Sarajevo, Zagorac managed numerous other clubs across Yugoslavia, including:
- NK Čelik Zenica
- NK Osijek
- NK Zagreb
- NK Velež Mostar
- FK Borac Banja Luka
- NK Rijeka
- NK Jedinstvo Bihać
Slavko Zagorac passed away in Zagreb, Yugoslavia (present-day Croatia) in 1988, leaving behind a profound impact on Croatian and Yugoslav football.