Slaven Bilic will not appeal against Cheikhou Kouyate's controversial red card in Saturday's 2-2 draw with Crystal Palace.
The West Ham boss said Kouyate's challenge on Palace substitute Dwight Gayle was not even worthy of a yellow card.
Bilic successfully appealed against the same player's dismissal at Blackburn in the FA Cup in February.
But he cut a frustrated figure after the 10 men were pegged back by Gayle's equaliser to dent their hopes of qualifying for the Champions League.
"Will we appeal? I am fed up with appealing," said Bilic.
"But make no mistake, I am very disappointed. This is the fourth time that this has happened. But we will go on fighting until the end of the season."
Kouyate will now miss next Saturday's visit of Arsenal, although Bilic could welcome back defenders Sam Byram and James Collins from injury.
The Hammers looked set to stay a point behind fourth-placed Manchester City after Manuel Lanzini cancelled out Damien Delaney's early header before a stunning Dimitri Payet free-kick put the hosts ahead.
But Gayle struck when Angelo Ogbonna and Winston Reid failed to deal with Pape Souare's cross to cost them two vital points.
"It's frustrating because in the first half I thought we were excellent and fully deserved to lead," full-back Aaron Cresswell told the club's website.
"In the second half the sending off changed the game and I think if that doesn't happen we win the game comfortably.
"Over the last four league games we've picked up three wins and a draw and it would have been nice to carry that form on.
"Unfortunately for us it wasn't to be and we're a bit disappointed that we haven't taken all three points."
Palace are now without a win in 14 games but manager Alan Pardew can see the finish line, believing they need four more points to be certain of avoiding relegation.
"I think, with our goal difference, we'll need 38 points," he said.
"I'm delighted for the team and they showed their heart is still very much in it. We've got ourselves into a bit of trouble but this was a great result."