The Premier League side could have nicked a crucial goal with six minutes remaining, when Chico Flores beat the offside trap as he ran on to Jonathan De Guzman's free-kick, but the Spanish defender's angled back header was straight at Napoli substitute goalkeeper Pepe Reina..
The two sides meet in the second leg in the Stadio San Paolo in Naples next Thursday.
Swansea face Liverpool in the Premier League at Anfield on Sunday, but Monk could be without his two standout players for the match, after Hernandez and Dyer both limped off with injuries. KEY MOMENTS
4’ Hamsik gets the ball in the centre of the box, but Michel Vorm in the Swansea goal is able to save down to his left. An early warning for Swansea about Napoli's threat on the counter.
5’ Cabral makes a great one-handed save from a shot by Dyer. That was an excellent response from the Welsh side.
39’ A short corner routine from Hernandez finds Williams at the far post, but the Swansea skipper heads over.
42’ Henrique breaks and sets up Canas, who finds Routledge. The former Spurs winger cuts inside and sees Cabral tip the ball over.
63’ Hamsik finds Callejon on the edge of the box, and the summer signing from Real Madrid beats Davies but toe-pokes his shot wide.
76’Reina makes a full-length save from Routledge's shot from the left channel, following a pass from Shelvey. But you get the feeling here that Napoli will hold on...
84’ Flores goes so close with a backward header from a free-kick from De Guzman, but the Spaniard puts the header straight at Reina. Where was the Napoli marking? KEY STATS
Napoli have not won on any of their nine trips to England, Scotland & Wales combined in major European competitions (L7 D2).
The Swans have failed to score in their last three Europa League games.
Did Swansea just miss their chance to take a scalp? On home turf, Swansea certainly did not look like European newcomers against a Napoli side packed with star power. But after failing to beat the Naples back line, they must get a result away to the Serie A side to progress. Garry Monk may have been the most satisfied manager on the performances front, but the result certainly leaves Rafa Benitez - the man who lifted this trophy last season with Chelsea - with the bigger smirk. MAN OF THE MATCH
Pablo Hernandez, Swansea - He bossed the Napoli midfield and was constantly feeding Nathan Dyer and Wayne Routledge on the wings with quick passes and showed great technique when picking up the ball under pressure further up the field.
Swansea: Vorm 7, Rangel 7, Chico 7, Williams 8, Davies 7, Britton 7, Canas 7, Hernandez 9, Routledge 7, Dyer 8, Bony 6. Subs: Shelvey 7, De Guzman 7, Emnes 6.
Napoli: Rafael Cabral 7, Maggio 7, Henrique 8, Britos 8, Reveillere 6, Dzemaili 7, Inler 7, Callejon 7, Insigne 6, Hamsik 7, Higuain 6. Subs: Reina 7, Mertens 7, Pandev 6.