.
Liverpool appealed against both decisions and now await the FA's deliberations over Carragher's foul on Bobby Zamora that saw him red-carded.
On the Degen case, an FA statement said: "At a Regulatory Commission hearing today, a claim for wrongful dismissal by Liverpool defender Philipp Degen was rejected.
"Degen was sent off for serious foul play during Liverpool's Premier League match with Fulham on Saturday 31 October. Degen's three-match suspension begins with immediate effect."
Degen will now be unavailable for the Premier League games at home to Birmingham and Manchester City, plus the Merseyside derby clash at Everton on November 29.
With fellow full-back Glen Johnson's calf injury forcing him out of Wednesday night's Champions League Group E clash in Lyon, Degen - who is not registered for Europe - could have found himself getting an extended run in boss Rafael Benitez's first-team.
Liverpool felt that Degen's foul on Clint Dempsey merited only a yellow card, but the FA do not agree.
If Johnson does recover in time for Monday's game with Birmingham, Degen will probably find himself completing the ban in reserve football.