Fresh from claiming only their second league win of 2015 last time out, West Ham missed out on an opportunity to build momentum at the King Power Stadium as Andy King's late strike secured victory for the hosts.
Cheikhou Kouyate had brought Allardyce's men level in the first half following Esteban Cambiasso's opener, but King grabbed the winner after both sides had seen chances go begging in an open encounter.
"Our failure to take our chances was why we lost the game in the end," said West Ham manager Allardyce.
"We came here to attack and create chances. We did that [but] we didn't take enough of our chances and ended up losing in the 87th minute.
"We had enough opportunities, so did they, it was a really open game.
"For a neutral it was fantastic, but from our point of view it's great to play open, attractive football and create chances, but the bottom line is we haven't got anything out of it.
"We're here as professionals and should have come away with at least a draw."
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