The Reds lost to Napoli with the same 1-0 scoreline last season and eventually went on to win the entire competition.
And Ancelotti reminded Klopp of that fact when they spoke after the game.
"I told him not to worry, because if he loses here, he tends to go on and win the Champions League," Ancelotti told Sky Sports Italia.
"I reassured him!"
On the match, Ancelotti added: "I want to see a team that believes in itself and its quality
"I really liked the way we played when we weren't in control.
"Llorente helped out. The players were tired and the first goal was from a long ball, which isn't our usual approach, but it's not an insult to do that sometimes. This team must know how to do everything."