 Nyorai kuenderera mberi kweiyi ndima - Pasi paCapellos Milan, Costacurta akaramba ari nhengo yekusingaperi yeiyo yekutanga line-up, uye akahwina mazita mana eSerie A mazita kusanganisira matatu akateedzana mazita muna 1991 92, 1992 93uye 199394, pamwe neimwe zita muna 199596, zita reChampions League muna 1994, UEFA Super Cup muna 1994, pamwe nematatu akateedzana eItaly Supercups muna 1992, 1993 na1994. Milan yakakwanisawo kusvika kumakwikwi matatu akatevedzana eChampions League pakati pa1992-93 na1994-95. Zvisinei, Costacurta akarasikirwa neChampions League yekupedzisira ye1994 kukunda Barcelona musi wa18 Chivabvu nekuda kwekumiswa, mushure mekudzingwa mumutambo we semi-fainari neMonaco. Costacurta akabatsirawo Milan kuhwina 1991-92 Serie A zita risingakundwi, sezvo Milan yakaenda pane rekodhi yeItaly yemitambo makumi mashanu neshanu isina kukundwa. Akaitawo basa rakakosha mumutsara wekudzivirira weMilan mumutambo wa1993-94, nekubvuma zvibodzwa gumi neshanu chete mwaka wese, sezvo Milan yakapedza mwaka iine dziviriro yakanakisa muItari. 