The Swans produced the better of the chances at the Liberty Stadium as interim boss Garry Monk, in just his fourth match in charge, took on the might of Rafael Benitez.
The chances kept coming for the home side but Ashley Williams was disappointed to head over the crossbar late in the first half before Wayne Routledge and Angel Rangel both forced action from the busy Rafael.
Napoli's best chances came when Marek Hamsik and Jose Callejon combined twice in quick succession but it was Swansea who again went closest as Williams saw another header miss, this time because of Reina.
The performance of the Welsh club was admirable against a Partenopei side who finished behind Arsenal and Borussia Dortmund in the Champions League but it may not be enough as they get set for the return bout at the Stadio San Paolo next week.
2013/14 UEFA Europa League - Round of 32 first leg
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