The defender was sent off for a reckless lunge on Enner Valencia during Sunday’s season finale and was dismissed by referee Michael Oliver.
Koscielny was slapped with a three match suspension for the straight-red offence – and that ban was upheld following an appeal process.
The Frenchman challenged the decision in a bid to make himself available for Saturday’s Wembley showdown with Chelsea.
An FA statement read: “Laurent Koscielny will serve a three-match suspension with immediate effect after a claim of wrongful dismissal was unsuccessful.
“The Arsenal defender was sent off for serious foul play during the game against Everton on Sunday [21 May 2017].”
Bizarrely, despite his dismissal – which came on a day when Arsenal had to win to have any chance of securing a top four spot – the 31-year-old was applauded off by sections of the north London support.
However, Arsenal secured the win, which was cancelled out by wins for Manchester City and Liverpool, meaning that they ended up finishing fifth.
Koscielny’s red card was his fifth in the Premier League since he joined the Gunners – no player has been shown red more during that time.