A James Milner penalty at the end of the first-half wasn't enough to overcome goals from Juan Bernat and Neymar.
Liverpool now must beat Napoli either 1-0 or, if the visitors score, by two goals or more to reach the knockout stages of the Champions League.
When questioned by reporters about the importance of the fixture taking place at Anfield, Ancelotti responded: “We must go to Anfield with courage and play our game.
“Now let’s think about the Serie A game at Atalanta on Monday, which will be more difficult than Liverpool.”
Ancelotti is one of many managers in recent times to deny the importance of the Anfield crowd.
Hoffenheim boss Julian Nagelsmann, Roma manger Eusebio Di Francesco and Man City's Pep Guardiola were all guilty of the same last season before eventually being defeated.
Whilst Napoli beat the Reds 1-0 in Naples and are a formidable side, Liverpool will always fancy themselves under the lights in front of their home crowd.