Savićević, officially a serving soldier at the time in the city of Skopje, made his competitive debut for Red Star during September 1988 in the European Cup first-round clash versus Irish champion Dundalk FC, scoring his first goal in the new uniform during the 3–0 return leg rout. Six weeks later, Savićević re-appeared in the epic second-round tie against A.C. Milan played over three matches in late October and early November 1988. He played a prominent part in the first leg at San Siro as Red Star played to a hard-fought 1–1 draw with Dragan Stojković scoring the valuable away goal. The return leg in Belgrade was even more eventful as Savićević had his team up 1–0 with an excellent strike, but German referee Dieter Pauly stopped and voided the match because of thick fog that engulfed the city. The second leg replay was played the very next day, resulting again in 1–1 scoreline, taking the match to penalties where the Italians came up on top 2–4 as Savićević and Mitar Mrkela failed to convert their spot-kicks.