Lorenzo Insigne, Arkadiusz Milik and Amin Younes scored as Carlo Ancelotti's side, in only their third friendly of the summer and their first against top-level opposition, cruised to victory.
The Reds left an awful lot to be desired at both ends of the pitch and, with less than a fortnight to go until they kick-off the new season at home to Norwich City, Jurgen Klopp will have concerns.
Story of the match
Napoli then raised their level and forced Simon Mignolet into a pair of saves, first from Simone Verdi and then from Insigne's free-kick.
Soon after, on 17 minutes Insigne produced a moment of real quality. Leading a Napoli counter, the Italian cut inside Joel Matip and bent the ball into the bottom-right corner from just outside the penalty area.
Liverpool failed to learn their lesson, allowing Insigne to get free down the left once more ten minutes later after conceding possession, and he was able to turn provider with a low cross which Milik slid past Mignolet.
The match settled to a pedestrian pace, and there was very little to excite the crowd, with the Reds looking disjointed.
At a stoppage in play, James Milner took an opportunity to gather his team-mates in the centre circle and demand an improvement.
There was a partial response before the break in the form of some livelier play and a disallowed goal for Georgino Wijnaldum, but Liverpool went in two goals down.
They predictably looked to start the second half with a greater intensity and enjoyed one or two openings, but the wind was taken out of their sails by Napoli's third.
Once again, Insigne had far too much space, and though Mignolet this time saved his curling effort, Younes was able to tap-in from the rebound.
Napoli could have had a fourth when Elseid Hysaj found himself with plenty of room in the area, but mercifully for Liverpool his cut-back was aimless.
Another chance went begging for the Serie A side owing to the swift reactions of Mignolet when Milik snuck in behind Matip.
In large part, the half was uneventful until the final ten minutes when a host of youngsters introduced from the bench, including new signing Harvey Elliott, sought to make something happen.
Despite rarely being tested, Alex Meret remained sharp and was able to prevent a Hysaj own goal before brilliantly turning Harry Wilson's driven effort round the post in the 90th minute.
Uncharacteristic defensive struggles continue
Liverpool shipped seven goals across their three games in the United States and any hope that they would tighten-up as their returning backline readjusted was swiftly extinguished in the Scottish capital.
Last year's Premier League runners-up looked alarmingly exposed every time they lost possession in midfield, and Napoli relentlessly found joy down the left-hand side.
Indeed, Trent Alexander-Arnold too often left his flank unguarded. He could on one or two occasions complain about a lack of cover from his midfielders, but generally he was careless in venturing forward.
With overlapping play from the full-backs integral to Liverpool's style, these lapses will simply have to be rectified in time for their season-opener.
Oxlade-Chamberlain left frustrated
For Alex Oxlade-Chamberlain, this summer has been about finding the rhythm after spending nearly a full season on the sidelines with injury.
At times he has looked capable of competing for a swift return to the starting XI - see his dazzling assist for Wijnaldum against Sporting - but his performance here confirmed that he is still some way off finding his best.
In short, nothing he tried came off, and he cut a somewhat dejected figure when he was substituted in the second half. The muted supporters struggled to stifle their groans.
In his defence, he was deployed in his less-than-favoured wing role, with Wijnaldum also unable to make an impression on the other flank. A call, one might say, for Klopp to invest in more natural, higher-quality cover for Mohamed Salah and Sadio Mane.
Promising glimpse of Elliott
On a positive note, Elliott looked bright in his brief cameo. The 16-year-old played with plenty of confidence and linked-up impressively with his new team-mates. It was not a coincidence that Liverpool upped their tempo after he came on.
He will get more opportunities to show what can he do before and during the season.
The Liverpool squad head to Evian this week for an intensive, and perhaps much-needed, training camp.
Klopp will hope to see a reaction from his team when they face Lyon in their final friendly in Geneva on Wednesday evening.
Then comes the curtain-raising Community Shield against likely title rivals Manchester City on Sunday.