The Reds were below their best against the Serie A side in their second fixture of Champions League Group C and were punished in the final minute when Lorenzo Insigne tapped in Jose Callejon's cross to take the points.
Finally, in the dying seconds of the match, Napoli managed to snatch a victor when Insigne latched onto a pin-point cross from Jose Callejon and tapped home from close range to earn a crucial 1-0 victory for the Italians. The Italian side will get their first chance against Liverpool on Wednesday.
"We have done it better this season, so we can do it - but we have to do it every game".
Liverpool goalkeeper Alisson had his work cut out on his return to Italy after his move from Roma last summer.
Sturridge's Reds teammate Salah has had a more hard start to the season and was hauled off by Klopp in the 66th minute at Stamford Bridge.
That's the view of former Reds midfielder Danny Murphy, who says the Englishman can be a big advantage for Jurgen Klopp this season.
Liverpool now turn their attention towards Sunday's encounter with Manchester City at Anfield as they look to maintain their unbeaten start to the league campaign. Remember Jay Spearing? The midfield bulldog who now plays his football for Blackpool in the third tier was a regular starter under Hodgson.
Liverpool finally started to find their footing midway into the second half, and Mohamed Salah should really have given them the lead in the 68th minute.