The points were shared in a 1-1 draw at Anfield on Wednesday after neither Liverpool nor Napoli managed to secure progression into the Champions League knockout stages.
Group E will now go down to the wire, with Champions League holders Liverpool, Napoli and Salzburg all still able to progress to the round of 16.
Napoli seem to have proved something of a bogey team for Liverpool in recent meetings, however, and inflicted the Reds' only defeat of the campaign so far back in September.
Klopp has lost three of his Champions League meetings with Ancelotti, his joint-most against an opposing manager along with Arsene Wenger, and conceded he struggles when going head-to-head with the Italian.
However, Liverpool's manager grew frustrated when asked who he thought would come out on top in the ring.
"I couldn't care less who would win a boxing match," Klopp told a news conference midweek.
"I am a couple of years younger than Carlo. If we were ever in a boxing match I'd hope I would win but I'm not sure.
"Obviously I struggle when I play Napoli so sorry about that. It's more about how good they are. That's how it is.
"Napoli usually play a different kind of football. Tonight they were defending and counter-attacking. It's not easy. When a team with the quality of Napoli chooses such an approach it makes life difficult. They probably would have changed if we had gone 1-0 up.
"Did I expect Napoli to be like this? Probably yes. Carlo is a smart guy. Napoli might not be in their best moment so you set up rather defensively and try to deny the strengths of the opponent and use your skills on the counter-attack. That's what they did for their goal.
"We spoke on the way to the dugout. And then after the game he wished me luck for the rest of the season and I wished him luck."
Liverpool need only to avoid defeat against Salzburg to seal their place in the next round. However, should they lose – and Napoli beat Genk – the defending champions would be at risk of dropping down to the Europa League.