 Crespo akabva kuRiver Plate achienda kuParma musi wa14 Nyamavhuvhu 1996 mushure mekunge awana menduru yesirivheri neArgentina kumaOlympics eZhizha 1996 uye akapedza semutambi wepamusoro zvibodzwa zvitanhatu. Akatadza kunwisa mumwedzi yake mitanhatu yekutanga mukirabhu uye aigara achirohwa, nemurairidzi mukuru Carlo Ancelotti achiuya kuzoshoropodzwa zvakanyanya nekuchengeta kutenda nekusarudzwa kwaCrespo. Kutenda kwake, zvisinei, kwakaruramisa Crespo akaenderera mberi nekukora ka12 mumitambo makumi maviri nenomwe mumwaka wake wekutanga weSerie A uye Parma akapedza ari wechipiri kuJuventus. Chinhu chinoshandura chakanga chiri kurumbidzwa kwaakagamuchira nokuda kwokubatsira kwake kurwisana neCagliari muna March 1997. Parma akakunda 1998-1999 Coppa Italia uye akarova chinangwa chekutanga muParmas 3-0 UEFA Cup yekupedzisirakukunda pamusoro peMarseille. Akanga arova zvibodzwa 80 mumwaka mina. 