The Swans' European adventure ended in Naples, but it was a proud effort from Garry Monk's side as they went down 3-1 at the Stadio San Paolo.
After Marvin Emnes saw his effort cleared off the line, Lorenzo Insigne gave Napoli a 16th minute lead after he beat the offside trap before chipping Michel Vorm.
But the Swans levelled through Jonathan de Guzman on the half hour, and the visitors ended the first half strongly.
Monk's side started the second half the better of the sides, and the visitors felt they had a strong case for a penalty as Dwight Tiendalli went down in the box under Raul Albiol's challenge.
Wilfried Bony then saw his header from a Pablo Hernandez cross fly straight into Pepe Reina's hands, in what was a decent opportunity for the Swans to stun the Stadio San Paolo.
But Napoli regained their lead with 12 minutes remaining as an attempted clearance from a cross deflected and dropped into the path of Gonzalo Higuain, and the striker blasted home from close range.
The Swans pushed hard for an equaliser and threw everyone forward, and it took an excellent block from Ben Davies to deny Higuain late on.
But Napoli would finish the contest in added on time as Gokhan Inler slid home under Vorm to claim a 3-1 aggregate win to progress into the last 16.
The Swans made five changes to their starting XI.
From the 4-3 defeat at Liverpool, head coach Garry Monk brought Dwight Tiendalli in at right-back as Angel Rangel moved to the bench while Ben Davies returned at left-back.
With Leon Britton missing out with a sore knee and Jonjo Shelvey not in the travelling squad due to a hamstring problem, Spaniards Jose Canas and Pablo Hernandez went into midfield.
The final change saw loanee Marvin Emnes given the nod on the right wing as Nathan Dyer was among the substitutes.
NAPOLI:Pepe Reina, Christian Maggio (capt), Henrique, Raul Albiol, Faouzi Ghoulam, Gokhan Inler, Valon Behrami, Lorenzo Insigne (Dries Mertens, 68), Goran Pandev (Marek Hamsik, 60), Jose Callejon (Miguel Britos, 84), Gonzalo Higuain.
SUBS: Roberto Colombo, Anthony Reveillere, Blerim Dzemaili, Duvan Zapata.
SWANS: Michel Vorm, Dwight Tiendalli, Chico Flores, Ashley Williams (capt), Ben Davies, Jose Canas, Jonathan de Guzman (Alejandro Pozuelo, 82), Pablo Hernandez, Marvin Emnes (Neil Taylor, 70), Wayne Routledge (Nathan Dyer, 62), Wilfried Bony.
SUBS: Gerhard Tremmel, Angel Rangel, Jordi Amat, David Ngog.
The Swans had settled into this contest in the early stages, though Lorenzo Insigne fired over after a surging 40-yard run, and then he set up Raul Albiol, but the defender nodded over when well placed.
Then the Swans carved open a great chance of their own as Pablo Hernandez raced on and fed Marvin Emnes in the box, but when the winger dinked his effort over the onrushing Pepe Reina it took a last-gasp clearance by Albiol to prevent the Dutchman.
But Napoli took the lead 16 minutes into the game as Insigne beat the offside trap to latch onto a ball over the top, and he chipped the onrushing Michel Vorm.
Things could have got worse for the Swans as Gonzalo Higuain fired wide when teed up by Goran Pandev.
But the Swans stunned the Stadio San Paolo on the half hour as Jonathan de Guzman levelled.
After Emnes cut inside and found Bony, the striker's one-touch flicked pass sent de Guzman in on goal, and the Dutchman's left-footed effort squeezed under Reina - who got a touch to the ball - and into the net.
It almost got better minutes later for Garry Monk's side, as Pablo Hernandez raced on towards goal but when he cut inside and let rip with his right foot, Reina comfortably dealt with the low effort.
And the Swans probed again as Bony's delightful pass cut through the Napoli defence with Routledge racing on, but the alert Reina raced out to clear the danger.
The visitors kept pushing for the lead, and when Henrique lost his footing when closing down Bony, the striker got himself into the box before firing a low effort which Reina again did well to keep out.
Bony, like he had in the first leg, was proving a constant menace and he showed his confidence by unleashing a 20-yard first-time effort on the turn after being fed by de Guzman, but Reina was untroubled.
It was a very strong finish to the half for the Swans, who will have been delighted with their performance in the opening 45 minutes.
HALF-TIME: Napoli 1 Swans 1
The Swans came out the stronger side after the restart and de Guzman was twice denied by Reina in the early stages.
A big moment arrived just before the half hour as Dwight Tiendalli reacted quickest inside the box and when he went down under Albiol's challenge the Swans felt they had a strong appeal for a penalty.
But Romanian referee Ovidiu Alin Hategan waved away the appeals much to the disbelief of the Swans bench.
Both sides made a change soon after as Marek Hamsik replaced Pandev for the hosts while Nathan Dyer came on for Routledge.
Then Hernandez again posed a threat as he jinked his way down the left before cutting inside and going for goal, but his effort was deflected wide for a corner.
The hosts didn't trouble the Swans until 20 minutes into the half, which was an indication of the strong start the visitors had made.
And it was Insigne who posed the threat as he tricked his way into the box before seeing his shot blocked for a corner by Chico Flores.
Then, at the other end, Emnes sent Hernandez racing down the left, and his perfect cross found Bony in the box, but his header dropped straight into the gloves of Reina.
The Swans made their second change with 20 minutes to go as Neil Taylor replaced Emnes, which saw the Wales international move to the left wing.
Then Napoli, who were enjoying a better period of possession, struck in rather fortunate circumstances in the 78th minute.
After substitute Dries Martens squeezed in a cross from the right, the defensive clearance cannoned off a team-mate and dropped to Higuain, who fired past Vorm from close range.
Monk made his final change as Alejandro Pozuelo replaced goalscorer de Guzman as the Swans went in search of another equaliser.
And they were denied in the final minutes by a superb reflex save by Reina, who tipped Tiendalli's header over from eight yards.
Then, at the other end, Higuain raced forward as the Swans were caught out at the back after throwing everyone forward.
The Argentinian squared to sub Marek Hamsik, and when the ball found its way back to Higuain, all that stood between him and Napoli's third goal was Ben Davies.
And the Welshman stood firm to deny the striker from point-blank range.
It was a tense finale, and Reina again denied Bony after the Ivorian met a loose ball in the box.
And then, deep into added on time, with the Swans throwing everyone forward, Napoli ended the contest.
Higuain took play down the left, and when he squared to Gokhan Inler, he slid his effort under Vorm.
That was the end of the action, and the Swans' European adventure.
With the final whistle blown, Hymns and Arias was proudly sung by the 900-strong Jack Army who had made the trip out to Naples.
And the Swans had done themselves proud in the competition too, with some memorable moments achieved along the way.