Arsenal's request to overturn Max Dowman's red card from the Carabao Cup tie with Fleetwood Town was rejected by the Football Association.
The Gunners had asked the FA to reverse Dowman's straight red for retaliating to a heavy challenge by Harrison Neal during their surprise defeat to the Cod Army on Tuesday night.
Arsenal argued that the dismissal was wrongful and the punishment excessive, but the FA affirmed that referee Michael Salisbury's decision was correct.
Dowman will now miss three consecutive domestic fixtures.
An FA statement said: "An independent Regulatory Commission has dismissed claims of both wrongful dismissal and excessive punishment for Max Dowman.
"The Arsenal player was sent off during their EFL Cup game against Fleetwood Town on Tuesday 27 October and will be suspended for three matches.
"The Regulatory Commission's written reasons for its decisions will be published in due course."
The suspension means Dowman will sit out Arsenal's upcoming matches against Liverpool at Anfield, Hull City at home, and Newcastle United at St James' Park after the international break.
He remains eligible for Arsenal's Champions League clash with Slavia Praha next Wednesday, as domestic bans do not apply to European games.
Manager Mikel Arteta's reaction to Dowman's first senior red card went viral, with the coach saying he had discussed the incident with the player before the game.
Arteta added: "I haven't seen it with the camera. You can't really see what happens."
He also noted: "The decision was made by the referee and that's it. And even with ten men, we have three big chances to score the second goal."
Arsenal are already short on width, with Bukayo Saka dealing with a quad problem, Noni Madueke nursing an ankle injury, and Christos Tzolis close to returning after a hamstring strain during the recent international break.
