The 1-0 defeat added to worries for coach Rafael Benitez, already under pressure after his team failed to qualify for the Champions League group stage.
Shortly after the playoff defeat by Athletic Bilbao, Italian media calculated that the club have sold only 6,500 season tickets for this season, one of the lowest totals in Serie A.
Benitez then raised eyebrows by taking a week off before the Chievo match, leading to rumours that he had fallen out with club president Aurelia De Laurentiis, although this was quickly denied by the club.
Although Napoli dominated the match, with Gonzalo Higuain having a first-half penalty brilliantly saved by Francesco Bardi, they failed to make their chances count and Maxi Lopez stole the points when he scored four minutes after the break.
It was all rather too familiar for Napoli fans whose side finished third in Serie A last season and won the Coppa Italia but were plagued by inconsistency.
They produced sterling performances to beat champions Juventus and runners-up AS Roma at home but undid the good work by allowing Chievo, Genoa, Parma, Sassuolo and Udinese to take points at the San Paolo.
"It's difficult to comment on this sort of defeat. We could have scored three goals in the first half," Benitez told Sky Sport Italia.
"We would be in difficulties if the team hadn't created anything but we had a penalty and 33 shots on goal. The truth is that we were just missing the goal.
"The whistling at the end of the match was an incentive for the next game," he added.
Continuing his round of television interviews, Benitez then tried to take the pressure off Argentina forward Higuain, a player who often looks as if he is carrying the world on his shoulders.
"We attack with lots of players and any of them can score goals, so it's not just a matter of waiting for Gonzalo to score," Benitez told Rai Sport.
Higuain is not the only player under fire and a section of the crowd booed misfiring forward Lorenzo Insigne when he was taken off during the second half.
"The fans today were fantastic with the team and they helped a lot, but we didn't reward them with a goal. It's the second match of the championship," added Benitez when asked if Napoli's title hopes were already down the drain.
"We had the right mentality at the start of the game but in the last 20 minutes we got a little bit hasty, we lacked tranquillity and that is something we have to work on."