A versatile defender, Picchi started to play in Internazionale as a right back, a role he previously held at SPAL. During the course of 1961–62 season, the legendary "Grande Inter" coach Helenio Herrera experimented by placing him as a libero. The new position was successful; he became an important figure in the team's strong defence, and indirectly set examples for teammates Tarcisio Burgnich and Giacinto Facchetti with his leadership. During that time, Internazionale was still captained by Bruno Bolchi.