The Atletico Madrid forward was booked in the 64th minute of Sunday's 2-2 draw at the Vicente Calderon for "simulation" under a challenge from Real defender Alvaro Arbeloa.
Atletico appealed the decision made by referee Carlos Delgado, but the Spanish Football Federation (RFEF) ruled on Friday that the caution was justified, which means Costa will now miss Saturday's clash with Celta Vigo as it was his fifth yellow of the season.
The striker, who made his Spain debut against Italy on Wednesday, will also have to pay a fine of €800, while Atletico will face a €350 charge.
"In the full viewing of the play in its various outlets it is not apparent that the cause of the fall of the player is contact with the opponent," a league statement read.
"So it does not disprove the contents of the referees report when he says the player simulated a foul.
"Accordingly the claims are dismissed, confirming the warning and disciplinary consequences."
Costa will not be the only player unavailable for Atletico coach Diego Simeone on Saturday, with Diego Godin and Arda Turan also serving one-match bans following bookings against Real.
