Manuel Lanzini's first-half penalty gave the Hammers all three points on home soil but it was a lacklustre affair.
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The game burst into life in the 24th minute when the hosts were awarded a spot-kick for a foul on forward Michail Antonio.
The Jamaica international looked to have nudged the ball out of play but he exploited a clumsy dash from Danish goalkeeper Nicolai Larsen to win the foul.
Lanzini stepped up and slotted home without breaking a sweat but that was about as exciting as it got.
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There were chances for West Ham but they were spurned with just five of their 15 shots on target.
And one miss baffled talkSPORT reporter, and famed Hammers fan, Ian Abrahams.
He told Kick Off: "They should have been 2-0 up but there was a criminal miss by Pablo Fornals a couple of minutes into the second half.
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"Literally he was passed the ball by a defender who didn't see him there and from 15 yards out he didn't even hit the target."
In the end, it didn't matter and David Moyes' men coasted to victory on a fairly dismal night in east London.
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"Let's face it, there's not many here tonight," Abrahams said with 30 minutes to go. "The game didn't really mean a lot and it's very expensive to come to football, as we already know, so the atmosphere is poor, the game is poor, it's like a training ground exercise."