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Liverpool remained in control of Group K with five points from their three games and two home matches still to come.
For Napoli it was their third straight draw and they will have their work cut out if they are to make the knock-out stages.
But in a lacklustre affair, Liverpool impressed with their organisation and discipline, especially given that Steven Gerrard and Fernando Torres were not even brought to Italy, Joe Cole started on the bench and Jamie Carragher lasted only the first half.
Prospect Jonjo Shelvey made his full debut while there were also starts for youngsters Jay Spearing and Martin Kelly.
The build up to the game was dominated by violence as a band of Napoli thugs prawled the city the night before the game randomly attacking Liverpool fans, resulting in five people being injured.
Once the match itself got under way, the first 45 minutes were thoroughly forgettable.
The most notable action until the final minute of the first period were a pair of speculative shots from the halfway line.
Edinson Cavani's for Napoli flew over Pepe Reina's bar while Shelvey's at the other end didn't even have the legs to reach the goal.
But right at the end of the half, Napoli came a whisker away from scoring.
Cavani got to the byline and pulled the ball back for Marek Hamsik but Paul Konchesky was perfectly placed to clear his close-range effort off the line.
The second half could not have been worse than the first and it proved not to be as Napoli played with a little more ambition.
Walter Gargano ran at the heart of the Liverpool defence on 54 minutes and slipped in Cavani but his rushed effort was easy pickings for Reina.
Christian Maggio then got down the right and crossed for Cavani but he put his header wide of the near post.
Up the other end Milan Jovanovic picked up a mistake by Salvator Aronica, drove at the Napoli defence and played Ryan Babel in one on one with Morgan De Sanctis but the Dutchman's lack of confidence showed and his finish on 69 minutes was weak.
On 81 minutes David Ngog brilliantly took down Jovanovic's chip into the box and turned his marker but his shot was blocked.
Europa League group stage results:
Group A
Manchester City 3-1 Lech Poznan - MATCH REPORT
Salzburg 1-1 Juventus
Group B
Atletico Madrid 3-0 Rosenborg Trondheim
Aris Salonika 0-0 Bayer Leverkusen
Group C
Sporting 5-1 Ghent
Lille 1-0 Levski Sofia
Group D
Villarreal 1-0 PAOK Salonika
Dinamo Zagreb 0-0 Club Bruges
Group E
Sheriff Tiraspol 0-1 BATE Borisov
AZ Alkmaar 1-2 Dynamo Kiev
Group F
Palermo 0-3 CSKA Moscow
Sparta Prague 3-3 FC Lausanne-Sport
Group G
Zenit St Petersburg 2 Hajduk Split 0
Anderlecht 3 AEK Athens 0
Group H
Young Boys 4 OB Odense 2
VfB Stuttgart 1 Getafe 0
Group I
Metalist Kharkiv 2 Sampdoria 1
Debrecen 1 PSV Eindhoven 2
Group J
Borussia Dortmund 1 Paris St Germain 1
Karpaty Lviv 0 Sevilla 1
Group K
Utrecht 1 Steaua Bucharest 1
Napoli 0 Liverpool 0
Group L
CSKA Sofia 0 Rapid Vienna 2
Besiktas 1 Porto 3
