While at Inter, Tagnin was part of the starting eleven of Helenio Herrera's "Grande Inter" side which won the UEFA Champions League final in 1964, during which he demonstrated his excellent man-marking abilities against Real Madrid's star player Alfredo Di Stefano. With Inter he also won two Serie A titles, in 1963 and 1965, as well as a second European Cup in 1965, and the 1964 Intercontinental Cup, making 56 appearances (36 in Serie A), and scoring 1 goal, which came in Serie A.