During his first spell at Parma, Asprilla scored 25 goals in 84 Serie A appearances. He is considered one of the greatest players of Parma's successful period in the 1990s. In his three full seasons with the club, Parma finished third, fifth and third in Serie A. The club also reached a European final in each of those seasons, as well as the 1994–95 Coppa Italia final. He also won the UEFA Cup Winners' Cup in 1992–93, as well as a runners-up medal in 1993–94 edition of the tournament, the European Super Cup in 1993, and the UEFA Cup in 1994–95 and 1998–99. In 1993, he was also ranked by FIFA as the sixth-best player in the world in the FIFA World Player of the Year award.