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Seven minutes into the game, Raheem Sterling appeared to have been felled inside the Tigers' box, but the referee turned down appeals for a penalty.
In the 25th minute, Emre Can drove forward before attempting to reach Balotelli with a pass, but the ball proved too far ahead for the Italian to latch on to, with Jakupovic claiming with ease.
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Chances became at a premium in the latter stages of the first half, with Adam Lallana and Joe Allen connecting well just after the half-hour mark, but the former lost his footing inside the box to kill off the move.
The second half began in lively fashion, with Sterling proving a handful on the wing and Liverpool's midfield weaving together some good passes, but Hull's defence was able to repel the bulk of those chances.
At the other end, Gerrard attempted a shot from distance, but it failed to trouble the Tigers keeper as it bobbled wide of the post.
In the 63rd minute, Balotelli missed a great chance when Sterling's flick floated beyond Jakupovic, but the 24-year-old was unable to head the ball into the back of the net.
The game appeared to peter out towards the latter stages, with concrete chances at a premium. Philippe Coutinho was played in by Gerrard in the 78th minute, but the subsequent effort failed to trouble the Hull keeper.
With just five minutes left, another penalty shout for Liverpool arose when Balotelli was felled in the box, but again, the referee waved away the appeals.
In a cruel twist of fate, Balotelli had a golden chance to seal the win in dramatic fashion right at the death, but Coutinho's ball into the box, requiring the simplest of tap-ins, stayed out despite the Italian being three yards out.