The Canaries created a number of chances at Upton Park but were repeatedly denied by goalkeeper Adrian before James Collins rose unmarked to head home and break the deadlock with six minutes left.
Mohamed Diame then sealed victory for the hosts deep into injury time to confirm a fourth successive game without victory for Norwich, who are now just one point above the Premier League relegation zone.
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"But you're relying on giving yourself a little bit of release and you can only do that by scoring goals.
"I don't think there'll be anybody watching the game who will have felt that we didn't attempt to get in the good areas, create chances, but it's been a little bit too familiar, this, where our level of performance has been good, we've been creating chances but not putting them away. That being the case you put more pressure on yourself."
Hughton also bemoaned his side's failure to prevent the Hammers' opener, adding: "What we haven't done well is on their first goal. It's a ball we dealt with very well all game but, on that one occasion, we didn't.
"That's what happens when you haven't got a lead you think you deserve - you're always putting yourself under that little bit of pressure, so I'm very frustrated.
"The second goal ... at that stage the players are so desperate to get back [into it], they're so frustrated we're behind in a game we shouldn't be that they've gone for it in that last few minutes but it was the first goal that hurt us, and the missed chances.
"They had chances but they had minimal chances. There's no doubt the best chances fell to us - there's no doubt about that. It's very frustrating because it's a game we shouldn't have lost.
"Their keeper made some good saves. Unfortunatelym in our last two away games, both [opposition] keepers have ended up putting in man-of-the-match performances so I think that shows we are creating chances but, if we are creating that amount of chances, we have got to be scoring goals."