Jugović was scouted by Red Star at the age of 15 by former Red Star player Toma Milićević. After making his debut for Red Star, he was loaned to FK Rad in the second half of the 1989–90 season. When Ljupko Petrović became coach of Red Star, Jugović was brought back to the starting eleven. In 1991, Jugović played in the 1991 European Cup Final, which Red Star won. Subsequently, he won the Intercontinental Cup as Red Star beat Colo-Colo 3–0, scoring the first two goals. By the end of his career with Red Star, he was awarded the Star of Red Star and became one of the most celebrated footballers in Yugoslavia.