The Swans, playing in their first-ever knockout round tie in European competition, turned in a spirited display but fell short at the San Paolo Stadium.
The hosts took the lead through Lorenzo Insigne before Jonathan de Guzman brought the Swans level on the half-hour mark.
Swansea squandered the chance to take the lead in the second half and were punished when Gonzalo Higuain put Napoli in front, before Gokhan Inler sealed victory for the Serie A side late on.
Victory sees Benitez, who won the competition with Chelsea last term, book a last-16 date with FC Porto, after the Portuguese side advanced virtue of the away goals rule following a 5-5 aggregate draw against Eintracht Frankfurt.
Swansea coach Garry Monk was hoping for another strong performance from his players after their impressive display in the goalless first leg in Wales last week.
The visitors almost went ahead in the 11th minute when Pablo Hernandez fed Marvin Emnes on the right side of the box and his goal-bound shot beat Pepe Reina, but was met with a goal-line clearance by Raul Albiol.
However, Napoli took advantage of a sluggish start from the Swans defence as Dwight Tiendalli and Ashley Williams were dragged out of line, allowing Insigne to beat the offside trap.
The Italian striker latched onto the end of a lofted ball before expertly lobbing Michel Vorm.
Napoli could not take their lead into the break, however, as Swansea found their stride and an away goal.
Parity was restored on the half-hour mark, when Wayne Routledge stretched the Napoli defence wide, before picking out De Guzman in the centre, who calmly slotted beneath Reina.
At the other end, Higuain's right-footed shot from the edge of the area went just wide of Vorm's near post.
Following the break, Napoli tried to attack before half-time but could not find a way through.
De Guzman was first to test Reina in the second half with a 20-yard effort which was saved by the keeper.
Their efforts were rewarded when Wilfried Bony cleverly sent De Guzman through and the Dutchman surged forward before drilling an 18-yard shot past an onrushing Reina to send 900 Swans fans at the stadium into raptures.
Swansea should have taken the lead midway through the second half when Hernandez, who continues to thrive in his newly-allocated No 10 role, provided Bony with a precision cross.
The Ivorian striker could not steer his header either side of Reina however and the on-loan Liverpool keeper collected with ease.
Reina then flew to clear Tiendalli's header from Hernandez's cross as Swansea squandered the opportunity to seize control of the tie.
Swansea were left to rue that miss when Higuain, benefiting form a lucky break as the ball fell at his feet from an attempted Ben Davies interception, fired home with venom to put Napoli in the lead.
The visitors came agonisingly close to making it 2-2 with two minutes remaining but Napoli goalkeeper Reina produced a fantastic one-handed save to repel Tiendalli's header.
Inler put the tie beyond any doubt when he scored his team's third seconds from time, as the Swans' European adventure came to an end.