Garry Monk - managing in Europe for the first time - witnessed his Swansea side put in a spirited performance in the first leg against the Serie A outfit at the Liberty Stadium on Thursday, but saw the likes of Wilfried Bony and captain Ashley Williams miss good chances to break the deadlock.
Rafael Benitez's Napoli started at a fast pace, but came close to going behind as Bony almost rounded goalkeeper Rafael Cabral before Williams headed over when unmarked at the back post.
Napoli headed into the match as favourites to progress and were looking for improvement after the break, but failed to put a stamp on the game and Williams again came close with a back-post header on 68 minutes.
Neither team was able to find a winner, however, leaving the tie nicely poised ahead of next week's return leg at the Stadio San Paolo.
The visitors had two opportunities to take the lead within the opening five minutes. Jose Callejon first dragged an effort wide from the right before a swift counter-attack led to Marek Hamsik forcing a smart stop from Michel Vorm with a strong left-foot shot.
After surviving that scare Swansea launched an attack of their own and a one-two between Nathan Dyer and Pablo Hernandez saw the former scoop an effort towards the far corner that Rafael did well to keep out.
Bony was proving to be a constant threat to the Napoli defence and the Ivorian sprung free of the defence on 22 minutes to latch onto Hernandez's throughball, but, after failing to round Rafael, his shot struck the goalkeeper in the face and went out for a corner.
Swansea skipper Williams had arguably the best chance of the half five minutes before the break. Hernandez's cross was played deep to the back post, where the centre-back had a free header that he put over the bar.
Rafael picked up an ankle injury shortly before the break, meaning regular number one Pepe Reina appeared in goal for Napoli in the second half.
By and large it was still Swansea who continued to control the tempo, although clear-cut chances were hard to come by after the interval.
Williams again almost found the breakthrough for Swansea with just over 20 minutes remaining when his towering header from substitute Jonathan de Guzman's free-kick forced Reina into action.
With 15 minutes remaining, Reina had to be on guard to keep the scores level when he parried Wayne Routledge's curling effort from the left-hand side of the box.
There was still time for one last chance for Swansea in the closing stages, but Chico Flores could only head De Guzman's free-kick straight at Reina from close range.
