Cornacchini initially played for Fano Fano between 1981 and 1987, and also had a spell on loan with Foligno during the 1985–86 season. After stints with Reggiana and Virescit Bergamo, he joined Piacenza in 1989, where he scored 36 goals in two seasons, finishing as the top scorer in Serie C1 on both occasions, and helping his team to win promotion during the 1990–91 season. His performances and prolific goalscoring attracted the attention of Serie A club Milan, by whom he was subsequently acquired in 1991; however, he often struggled to find space in the team's starting XI under manager Fabio Capello, due to the presence of established forwards such as Marco van Basten and Ruud Gullit; he obtained only three league appearances, making his club and Serie A debut on 15 September 1991, in a 1–1 away draw against Juventus in Turin, as Milan finished the 1991–92 season as Serie A champions.