Carlo Ancelotti’s charges were beaten 3-1 at Juventus, the title-holders in Serie A, on Saturday evening despite taking a 10th-minute lead through Dries Mertens.
A double from Mario Mandzukic either side of half-time overturned the visitors’ advantage, before they lost Mario Rui for a second yellow card and Leonardo Bonucci ensured the points with a third goal.
Napoli had won back-to-back league matches in the week before their defeat in Turin; they claimed a 3-1 victory at Torino and saw off Parma 3-0 at home.
The Partenopei began their Champions League Group C campaign with a goalless draw against Red Star Belgrade and therefore trail Liverpool, who beat Paris Saint-Germain, by two points.
The clubs have only met twice before in competitive football, in the 2010-11 Europa League group stage, when Liverpool won 3-1 at Anfield and drew 0-0 in Naples.
Jürgen Klopp’s team achieved a 5-0 result in a friendly between the sides in Dublin in August.