Tancredi made 282 appearances for Roma from 1979 to 1990. Although not very tall for a keeper Tancredi was blessed with great speed and agility and was a penalty save specialist.
He was the number two goalkeeper to Giovanni Galli in Italy's squad at Mexico 86. He made a total of 12 caps with the national team.
In 1987, during a game against A.C. Milan at the San Siro, he was hit on the head by a firework thrown by a Milan supporter. He stopped breathing for a short time but was eventually resuscitated by paramedics.
After retiring as a player, Tancredi worked as a goalkeeping coach for Roma until 2004 before following coach Fabio Capello to Juventus F.C. and taking the same post. At the start of the 2006-2007 season Tancredi followed Capello to work as a goalkeeping coach at Real Madrid.
On 14 December 2007 he was formally appointed the Goalkeeping Coach of England in line with the appointment of new Manager, Fabio Capello.