Known for tenacious defensive skills, Radović started playing basketball at OKK Belgrade where he went through all age groups with the club's youth system. Among the different coaches he worked with at OKK Belgrade, Radović got coached by Vlade Đurović who would go on to a significant coaching career.
After his NCAA adventure, Radović came back home, signing with Red Star Belgrade where he spent 9 seasons (1981–1990) and grew into a dependable point guard as well as a defensive stalwart on the Yugoslav national team. In addition to the suffocating and aggressive defensive style, the staple of his game was going after offensive rebounds, a practice he picked up while playing college ball and introduced to the Yugoslav League where guards at the time rarely engaged in such forays on offense.
In 1990 he moved to Berlin, spending two seasons at the developing German club Alba Berlin.
In 1992 he came home to Belgrade again and, after a season in Pavia (1993/1994), finished out his career with a club where he started it - OKK Belgrade.