Burnley are now without a win from eight Premier League matches in 2014-15, but they were on top for much of the first half at Turf Moor.
George Boyd struck the crossbar in the opening five minutes and Lukas Jutkiewicz had a goal ruled out for offside as Burnley began brightly, but they failed to turn their superiority into goals.
West Ham responded strongly in the second half and headers from Diafra Sakho and Enner Valencia put them in control.
Boyd did pull one back for Burnley, but Carlton Cole's effort made it 3-1 with 20 minutes remaining and Dyche was left to rue his side's missed opportunities in the first half.
"Unfortunately we're learning the hard way," he said. "The harsh reality of the Premier League is you have to take your chances.
"It was a very good display in the first half, with the energy and quality of the play and the chances we created.
"We hit the bar and a number of chances go by and you know that second half you've got to come out quicker than that and we didn't.
"You can't afford to have a soft 15 minutes in the Premier League and it was two moments of quality from them, it must be said, great crosses.
"We've got to make sure we score more freely. It's within us, it's just getting it onto a football pitch and making sure we show clarity to score goals.
"My job is to find the positives but not be naive enough to not accept the things we've got to change. We've got to believe in what we're doing and I certainly do.
"We work really hard and I thought we did today but you've got to make sure when you're dominant like we were in the first half you take your chances."
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