 Albertini akakunda mazita akawanda mumakore ake kuMilan, uye akatora mazita matatu akatevedzana eSerie A muna 1992, 1993 na1994, uye akakwanisawo kutora mamwe maviri scudetti muna 1996uye 1999. Mukuwedzera, akaita 41 Champions League kuonekwa, achibatsira Rossoneri kusvika matatu akatevedzana magumo pakati 1993 uye 1995, vachisimudza mukombe muna 1994. Akakundawo UEFA Super Cups mbiri, Italian Super Cups nhatu, uye Intercontinental Cup panguva yake yekirabhu. Albertini akaramba ari kuMilan kusvika 2002, apo maneja wake uye aimbova mudzidzisi Carlo Ancelotti akasarudza kutamba Andrea Pirlo ari kubuda panzvimbo yake. Munguva yake yekirabhu, akakwanisa zvibodzwa makumi maviri nesere mumitambo makumi mana nematanhatu; akahwinawo rekodhi yemunhu zvibodzwa zvisere mumwaka wa 28-1996. 