Liverpool defender Degen was dismissed late on in the 3-1 defeat at Craven Cottage on Saturday after a lunging challenge on Clint Dempsey.
The Anfield outfit felt referee Lee Mason had been harsh on the full-back and were keen to see the offence downgraded to a caution.
But the Football Association's regulatory commission have agreed with Mason's verdict and Degen must now serve an immediate three-match suspension.
Rafa Benitez will now be without Degen's services for the Premier League clashes with Birmingham, Manchester City and derby rivals Everton.
At the same hearing, the FA upheld claims of mistaken identity from Manchester United's Fabio Da Silva and Aston Villa's Stephen Warnock.
Da Silva's booking in the Carling Cup victory over Barnsley at Oakwell has now been transferred to his twin brother Rafael, while Warnock's caution in the draw with Everton now rests with team-mate Stiliyan Petrov.