Despite a promising start at the San Paolo, the hosts were wasteful in front of goal and paid the price.
Coach Maurizio Sarri says a more "carefree" approach could help Napoli unlock a Champions League last 16 place after a 3-2 defeat at home to Besiktas kept the Italians waiting.
Napoli welcomed the Turkish champions knowing a third consecutive Group B win, along with a Dinamo Kiev-Benfica draw, would secure entry to the knockout phase with three games to spare and set a new competition record.
But despite a promising start at the San Paolo, the hosts were wasteful in front of goal and paid the price for a glaring Jorginho blunder that saw Cameroonian forward Vincent Aboubakar give the visitors a 2-1 lead by the 38th minute.
Manolo Gabbiadini, demoted to the bench in place of Dries Mertens after 3-1 defeat to Roma last weekend, struck the leveller on 69 minutes after Lorenzo Insigne had missed the chance to equalise from the spot shortly after the restart.
But Napoli failed to capitalise on further chances and paid the ultimate price when Aboubakar headed Ricardo Quaresma's free kick past Pepe Reina four minutes from the end.
Besiktas' first group win since 2009 kept them in second place to sit just one point behind Napoli and they will be looking to relaunch their last 16 bid with a win next month.
Coach Senol Gunes said: "Now we have to face Napoli at home but it will be hard to get out of this group."
Defeat for Napoli at the Vodafone Arena in Istanbul would spell disaster for the Azzurri on their first appearance in the group stages since 2013 when Walter Mazzarri's side were eliminated behind Borussia Dortmund and Arsenal.
After their third consecutive defeat in all competitions, Sarri says a more "carefree" approach to their trademark flowing game could help settle nerves.
"We have to react and try to find a more carefree approach to our game," said Sarri.
"Tonight we made life difficult for ourselves. We should be enjoying these games without feeling too much pressure. Unfortunately the lads felt the weight of expectation.
"We had the right level aggression and I saw some good stuff in attack, but we have to defend with a little more order."
Mertens had hit a brace in a 4-2 win over Benfica a fortnight ago and was handed a rare start in the striker's role after Gabbiadini failed to impress against Roma.
The Belgian was their biggest culprit in front of goal, but he soon vindicated Sarri's decision to leave Gabbiadini on the bench with a series of early chances, notably firing just over from 12 yards.
But Besiktas breached the Napoli net after just 12 minutes when Adriano powered through to fire Quaresma's superbly-weighted ball past Reina after the Portuguese capitalised on a defensive mix-up.
Mertens went on to miss three times in succession before powering past his marker to meet Jose Callejon's perfectly-weighted delivery from the right to sidefoot past Fabri from close range on the half hour.
Eight minutes later Aboubakar pounced Jorginho's howler to beat Reina for a 38th minute lead.
Sarri refused to blame the Brazilian midfielder, adding: "Jorginho misplaced one pass and unfortunately for us it was a crucial one. But when you make 130 passes in a game, that can happen."
A Fabri foul on Mertens gave Napoli a penalty just after the restart but Insigne bundled a tame effort straight at the 'keeper.
Gabbiadini replaced Insigne on 65 minutes and four minutes later coolly stepped up to beat Fabri from the spot after Caner Erkin had fouled Mertens.
Napoli could have wrapped up a great comeback win but Gabbiadini was ruled offside after beating Fabri at the second attempt and Mertens fired a sizzling shot wide of the far post after outfoxing his marker.
The hosts paid the price in the 86th minute when Aboubakar rose at the far post to meet Quaresma's delivery to beat Reina for the second time.