The Reds will host the Toffees at the beginning of next month as Premier League sides enter the competition.
But Carragher is not worried about Jurgen Klopp’s side facing another Merseyside derby in the New Year.
He tweeted: “Delighted! We can f**k EFC’s Xmas & New Year up!!”
Liverpool welcome Everton to Anfield this Sunday in the Premier League.
And Carragher clearly thinks the Reds can do some damage to the Toffees who have won their last two in the top flight.
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The Merseyside derby wasn’t the only cracking tie to come out of the hat for the FA Cup third round.
Brighton and Crystal Palace will also face off as holders Arsenal travel to Nottingham Forest.
Chelsea travel to Norwich, Manchester United host Derby and Manchester City face fellow Premier League side Burnley.
AFC Fylde could face Premier League outfit Bournemouth if they beat Wigan in their replay while Hereford will take on Leicester if they get past Fleetwood.
Liverpool’s next challenge is in the Champions League against Spartak Moscow on Wednesday as they look to secure top spot in Group E.