Hull dominated the first half at Upton Park but failed to score, Sone Aluko the main culprit, and Andy Carroll, Morgan Amalfitano and Stewart Downing all found the net for the Hammers in the second period.
Defeat means Hull are 18th in the table and now have won just twice in 15 league matches.
"The way we played in the first half delighted all of us connected with Hull but in my experience you have to score," Bruce said.
"For all the good work we did, it unravelled really. You can't let them off the hook like that.
"You come away from home, play against a good team like West Ham and have two or three good opportunities to score and we didn't.
"That's the disappointment and frustration for us all."
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