After beginning his professional career with Juve Stabia and Palmese, Nappi played for 8 seasons (172 games, 1 goal) in the Serie A for Perugia Calcio (1974–1982; 1984–85) and A.S. Roma (1982–84). Most of his career was spent with Perugia, where he won the 1974–75 Serie B title, and was a part of the 1978–79 Serie A season in which Perugia finished the season unbeaten, but still finished second in the league, behind A.C. Milan. After leaving Perugia in 1982, he spent two seasons with Roma, before returning to Perugia for a final season. With Roma, he won the Serie A championship, the Coppa Italia, and reached 1984 European Cup Final, in which Roma were defeated by Liverpool F.C. in the resulting penalty shootout.