Ivan Toney poked Brentford ahead in the 19th minute after West Ham failed to deal with a long throw, then Josh Dasilva made it 2-0 as West Ham were booed off at half-time and full-time.
West Ham have now lost five consecutive Premier League matches and Moyes will now have to revise his opinion last week that the Irons were not in a relegation battle. If results elsewhere go against them over the weekend they could be bottom of the table on New Year's Day.
Following the defeat Moyes' odds were cut from 6/1 to 8/11, and the 59-year-old Scot is now ahead of Everton manager Frank Lampard (11/10) in the next Premier League manager to be sacked market.
Earlier in the week Moyes had confidently stated that he was not under pressure at West Ham despite the club sitting just above the Premier League relegation zone following an indifferent set of results.
Moyes had credit in the bank with co-owner David Sullivan after guiding West Ham to sixth and seventh-placed finishes, as well as a Europa League semi-final just seven months ago. "Am I under pressure at the moment? No, not at all. I've got great support from David Sullivan," said Moyes on Thursday before the Brentford match. "I'm not daft, you are always under pressure as a football manager. Nobody can get over that. Most managers, if you lose a few games, you are always going to be under a bit of pressure."
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