It was the Reds fifth loss in the league this season and leaves them in fifth place nine points behind leaders Chelsea after 11 matches.
"We will try to appeal against both red cards because for me it's very clear that Carragher was kicking the ball and the other one Degen was not kicking the player," Benitez told the club website.
With Liverpool losing 2-1 following Erik Nevland's strike, Swiss fullback Degen was the first to go after 79 minutes when referee Lee Mason showed a straight red for his late challenge on Fulham midfielder Clint Dempsey.
Three minutes later the visitors were reduced to nine men, after Carragher's challenge on striker Bobby Zamora was deemed a professional foul, before Dempsey added a third goal.
"For me, the first one with Degen was a yellow card, and with the second one it was clear that Carra was kicking the ball and not Zamora," Benitez added. "I watched the replay and it is clear."
Fulham had taken a first-half lead through Zamora before a Fernando Torres equaliser just before the break, but the visitors faded badly when the Spaniard was replaced on the hour.
Torres played in last weekend's 2-0 win over Manchester United, a result that had appeared to haul them back into the title race, despite fitness worries and Benitez had not expected him to feature for the full match at Craven Cottage.
"After this game he needed four days to be ready again but he still isn't 100 percent fit, so we had to decide if he could start today or use him for part of the second half. We decided to start with him but I have to protect the player."
"We decided to take him off just after the hour because I want to protect him and don't want to lose an important player like Fernando for one month. We had options in attack when he came off."
One of those was 18-year-old English striker Nathan Ecclestone who came on to replace Yossi Benayoun with 12 minutes remaining for his league debut.
"We now have a difficult (Champions League) game against Lyon. My concern now is we have too many injuries and we have to analyse which players will be available for Wednesday," added Benitez.
Liverpool were without six first-team players for Saturday's match including injured captain Steven Gerrard and defenders Glen Johnson, Martin Skrtel and Daniel Agger.
They travel to French side Olympique Lyon on Wednesday having lost two of their first three Group E games this season.
