Walter Mazzarri's side sealed their third consecutive draw in Serie A and now trail the Scudetto leaders by six points
The Partenopei only managed to test Udinese goalkeeper Daniele Padelli once in the 90 minutes in a match that lacked goalmouth action.
Udinese welcomed back Emmanuel Agyemang-Badu after Ghana's Africa Cup of Nations campaign whilst Danilo returned from suspension to take his place in the heart of defence.
Napoli were unchanged from the side who drew 0-0 with Sampdoria in their last league outing, fielding three former Udinese players in Morgan De Sanctis, Gokhan Inler and Pablo Armero.
Mazzarri's side almost got off to the worst possible start after three minutes when Giovanni Pasquale capitalised upon an error from Giandomenico Mesto to latch onto Antonio Di Natale's through pass, but the 31-year-old could only drag his right-footed effort wide of the post.
Edinson Cavani, the division's highest goalscorer, had not scored in his last five matches and he really should have ended his personal goal drought moments later but the Uruguayan talisman uncharacteristically failed to get on the end of Mesto's teasing right-wing cross.
Udinese were looking to expose the three-man Partenopei defence with searching balls into the wide positions and Di Natale showed his predatory instinct to dart in behind Miguel Britos before fizzing a wonderful half-volley narrowly over the crossbar.
Napoli have endured a recent slump, having scored only once in their winless streak of four matches in all competitions, and it took Mazzarri's side until the 36th minute to muster the game's only shot on target. Marek Hamsik was looking to cap his 250th Napoli appearance with a goal but the Slovakian was denied when his header from Armero's left-wing cross was smartly beaten away by Daniele Padelli.
In a scrappy first half devoid of presentable goalscoring opportunities, the Zebrette had the chance to open the scoring two minutes before half-time when Di Natale seized onto Agyemang-Badu's neat slide pass, but the 35-year-old captain could only fire his left-footed effort over the crossbar.
Udinese are well-renowned for their counter-attacking abilities and they nearly stole ahead five minutes after the break when substitute Thomas Heurtaux broke forward from defence and Roberto Pereyra really should have found the back of the net after Di Natale's deflected effort fell his way inside the Napoli box.
Mazzarri knew that his side could ill-afford to drop any more points in the Scudetto race and he cut a frustrated figure on the sidelines, urging his side to push forward. Hamsik witnessed his ambitious volley flash wide of Padelli's goal before Lorenzo Insigne's goal-bound effort was deflected inches past the post as Napoli strived to break the deadlock.
The 51-year-old coach was then left seething when Armero went tumbling in the penalty box under a challenge from Dusan Basta, but referee Antonio Damato adjudged the Colombian wing-back had dived and duly cautioned the former-Udinese star.
The visitors were beginning to take control of the contest and it looked as though they would open the scoring when Armero found space in behind Basta, but his cutback was fed slightly behind Cavani who could only steer the ball wide of the left-hand post.
Mazzarri threw on Goran Pandev and Juan Zuniga in a bid to snatch a late winner, but he watched his side fail time and time again to break down a resilient Zebrette defence, and the game finished all square.
Napoli face a potential title-decider when they entertain table-topping Juventus at Stadio San Paolo on Friday night.