Bellingham banned for two games after red card in Valencia draw
Madrid appealed against his red card but the federation's disciplinary committee dismissed their complaint that referee Jesus Gil Manzano made an "error" by dismissing Bellingham.
The England international, La Liga's top scorer with 16 strikes, netted moments after the referee blew for full-time in Madrid's 2-2 draw at Valencia.
Bellingham, 20, ran over to the referee insisting the goal should stand and was sent off, with Gil Manzano saying he showed an "aggressive attitude" and was "shouting".
The midfielder misses upcoming La Liga games against Celta Vigo and Osasuna.
Real Madrid lead the top flight by seven points ahead of Girona and are eight in front of rivals Barcelona, third.