The 26-year-old Switzerland international was dismissed in the closing stages of the Craven Cottage encounter for his late challenge on Clint Dempsey.
Degen will now have to serve a three-match domestic ban but is available for Wednesday's Champions League game in Lyon.
Jamie Carragher was also sent off against Fulham, as the Reds ended the match with nine men, for his tackle on Bobby Zamora.
However, the FA is still to make a decision on Liverpool's appeal against Carragher's dismissal.
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Meanwhile, captain Steven Gerrard has admitted that the summer sale of Xabi Alonso to Real Madrid did come as a blow to the team.
He told FourFourTwo magazine when asked about his reaction to the Spain international's departure: "Devastated. But there was nothing I could do about it.
"Xabi said a long time ago that he wanted another chapter in his career and finally he got it and his team-mates and the coaches couldn't stand in his way.
"We just have to say thanks and move forward without him.
"It's always going to be different when you lose one of the best players in the world - and people are finally realising that's what he is, on the back of his form for Real Madrid and the difference in us from last year.
"We've got other midfielders here doing a good job but it will take a while before Alonso's out of our system because he was such a top player."