Hull City 0 Liverpool 0
Ian Dowie's relegated side finish 19th in the table while Rafa Benitez's men have to settle for seventh place.
Hull's Tom Cairney came close to scoring an own goal early on when his sliding challenge on the edge of the Tigers box sent the ball flying just wide of keeper Matt Duke's left-hand post.
Nabil El Zahr almost put Liverpool in front on 20 minutes but his arrowed right-footed shot from the edge of the box was turned over the bar by Duke.
Dirk Kuyt then came close moments later as El Zahr found the head of the Dutchman with a miscued shot but the frontman's effort from close range was neatly headed off the line by Hull skipper George Boateng.
Alberto Aquilani was next to go close for Liverpool when the ball fell to the ex-Roma man just outside the box but his first-time right-footed effort flashed just wide of the right-hand post.
Hull had a great chance to take the lead towards the end of the half when a pin-point cross from Will Atkinson found the head of an unmarked Mark Cullen inside the six-yard box but the Tigers youngster failed to hit the target, sending the ball inches wide of the right-hand post.
Benitez's men could and should have taken the lead on the stroke of half time when first Aquilani hit the crossbar with a right-footed shot from just inside the box.
An unmarked Daniel Agger then had a great chance to net the rebound but the Denmark international could only send the ball high and wide of the Hull goal from close range.
Hull came within inches of opening the scoring just after break as Bernard Mendy's cross found the outstretched leg of Jan Vennegoor of Hesselink but the Dutchman could only send the ball just wide of the left-hand post.
Mendy came close himself on the hour mark but his thunderous right-footed effort from 35 yards was neatly turned over the bar by Pepe Reina.
Steven Gerrard came close late on for Liverpool but his 18-yard shot hit the outside of the left-hand post and went out for a goal-kick.