The Football Association has turned down appeals from West Ham and Liverpool for wrongful dismissal for Hayden Mullins and Luis Garcia.
Mullins and Garcia were sent off eight minutes from time
Mullins, 27, and Garcia, 27, were sent off for clashing in Wednesday's league match and now miss the FA Cup final.
Hammers' manager Alan Pardew and Reds' boss Rafael Benitez asked the FA to show leniency straight after the game.
But a disciplinary commission hearing on Friday rejected the claims and both players will serve a three-match ban.
Garcia appeared to aim an elbow at fellow midfielder Mullins' back before going to ground after a shove by his rival as the duo fought for the ball eight minutes from time.
Pardew said: "I feel very aggrieved and very upset because Hayden has had a fantastic season. He has been one of our best players.
"He was my first signing here, I'm very proud of him, of what he has done and achieved.
"I for one will be very sad if he misses the final and I know Hayden will be feeling a lot worse than I will be."
Benitez added: "Luis is very disappointed. I said to him after the game that he had made a big mistake as you can't lose your control before important games.
"Maybe for the future this will be good for Luis and the rest of the players because they can see what could happen.
"It is a big blow for us as he is a player who scores goals on important occasions. He can change a game and so of course we are going to miss him in Cardiff."