Lorenzo Insigne was the hero in Naples, where Napoli got their European campaign on track thanks to the star forward's 90th-minute winner on Wednesday.
Last season's runners-up Liverpool were below their best throughout the Group C clash as Napoli – who were held to a goalless draw by Red Star Belgrade on matchday one – claimed a deserved three points after Dries Mertens rattled the crossbar moments earlier.
Ancelotti revelled in the victory afterwards, particularly pleased with the manner of Napoli's triumph over the Premier League giants at Stadio San Paolo.
"The team did well throughout the game, we never lost control, were always very focused, above all when defending and allowed Liverpool practically nothing," Ancelotti told Sky Italia .
"We had the chances to score earlier, but I think we timed it well. We scored at the right time… If Mertens had scored a few minutes earlier, it would've been more time suffering!"
Ancelotti added: "It means a lot to us to have won against the finalists from last year.
"It's important for the confidence of the players, and these games give extra focus, but also some worries. I just told them to enjoy themselves, and it went well.
"We showed this group won't just be hard for Napoli, but for everyone involved. After the disappointment of the first game, this is a great injection of confidence, but there's still a long way to go in this group."
It was a moment to savour for local favourite and Italy international Insigne, who slid on to Jose Callejon's low cross as he prodded the ball past Liverpool keeper Alisson.
"It's wonderful to win like this, but we had a great performance as a team and wanted the result at all costs," Insigne told Sky Sport Italia.
"Now we'll enjoy this victory for a little bit, because we have to focus on Sassuolo, which will be another really tough one."