Upon joining Red Star, he was loaned to FK Rad for the whole 1989–90 season. When Ljupko Petrović became coach of Red Star, Jugović was returned 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. 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.
In the 1997-98 season he joined Lazio spending only one season with the Roman club winning his second Coppa Italia 1997–98 Coppa Italia beating Milan in the 2-leg final, also the club reached the Uefa Cup final 1997-98 UEFA Cup losing in the final to Inter in the all Italian final.