Despite dominating the second half and creating three or four excellent goalscoring chances, Hammers couldn't find the breakthrough for the second week running and were punished for their failure to score.
Leicester had made the better start and scored what proved to be the only goal of the game in the 25th minute, but the hosts couldn't have complained if they had ended up losing after a one-sided second half that left Tony Carr frustrated by his team's performance.
"We played a lot better today than we did last week," he said, "but once again we had the problem of not being able to convert some clear cut chances in front of goal.
"We dominated the second half and it wouldn't have been an injustice if we had won 3-1. That's the way it goes, though, and we are suffering a bit of a difficult spell at the moment."
Team: Jackson, McClenahan, Tattam, Parrington, Laws, Lumsden, Akinsete (Khan 70), Carrick, Pearson (Wright 75), Morris (Mehmet 70), Cole. Subs unused: Sealey, Bunce.