The Addicks defeated the Reds 3-2 on Saturday.
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Liverpool will be disappointed being dumped out of the competition in only the third round.
Charlton jumped to a 3-0 lead through captain Jack Belton, Ellis McMillan and Bradley Tagoe.
Liverpool fought their way back late into the second-half through goals from Josh Sonni-Lambie and Finn Inglethorpe, but it wasn't enough.
Charlton will go to the winner of the tie between Plymouth and Watford in the fourth round.