The France international, 29, was sent off in the 13th minute at the Tottenham Hotspur Stadium after a late challenge on Spurs captain Micky van de Ven.
Mateta was originally shown a yellow card by referee Michael Oliver, but it was upgraded to red following a VAR review.
He will be suspended for Palace's league match at home to Liverpool on Sunday, in addition to fixtures against Coventry and Hull later this month.
A statement from the Football Association said: "An independent regulatory commission has dismissed claims of both wrongful dismissal and excessive punishment in relation to Jean-Philippe Mateta."