He is the second the all-time leading goalscorer for Atlético Madrid with 169 goals, having appeared for the club in 13 La Liga seasons and played in more than 350 official games.
On 8 March 1953, Escudero netted Atlético's 1000th goal in the top division, in a 2–3 away loss against Celta de Vigo, through a penalty kick.
After the sacking of Rafael García Repullo (his former teammate) early into the 1963–64 season, he was an interim for one round, a 1–2 defeat at Valencia CF on 29 December 1963.
[2] Escudero earned three caps for Spain in three-and-a-half years, his debut coming on 7 December 1952 in a friendly with Argentina played in Madrid (0–1 loss).
In his only official appearance, on 17 March 1954, he scored against Turkey for the 1954 FIFA World Cup qualifiers – the third playoff match ended 2–2 in Rome, and the Spaniards were eliminated after a drawing of lots.