He was sent off in the 58th minute after an out of control lunge on Lucas Moura, with no attempt made to play the ball, during Tottenham's 1-o win at Wembley.
The red card was widely seen as just, but Cardiff did not agree.
Speaking after the game, veteran manager Neil Warncok described the dismissal as "very soft" and said that Harry Kane had been "trying to make an issue of it" by reacting to the incident.
In the wake of Warnock's comments, the 'Bluebirds' tried to have the decision overruled, but the FA rejected their appeal.
After having his ban upheld, Ralls will miss the club's upcoming fixtures against Fulham, Liverpool and Leicester.