Winston Reid's first-half injury naturally disrupted the team, with the centre-back down for ten minutes before being stretchered off the pitch after a tackle inside the box.
Reid had missed West Ham's previous match through illness.
"The fans travelled through the snow to get here and we let them down badly", Moyes added.
The Hammers now sit in 14 in the Premier League table, just three points above the relegation zone with nine matches of the season left to play.
Swansea City, though, are inadvertently complicating matters with their surprising FA Cup run.
West Ham have been dragged back into the thick of the relegation battle after back-to-back 4-1 defeats to Liverpool and the Swans.
The Dutchman could not believe his luck as he headed home unchallenged at the far post from Ki's corner. They were sluggish, unfortunate, beaten.
And they were breached early with Andre Ayew laying the ball off for Ki, whose shot lacked venom but was placed perfectly to beat Adrian and slowly creep over the line.
'Andre wanted to show something against his old team, ' said Mike van der Hoorn, who gave Swansea a two-goal cushion before the break with his second goal in English football. They have no new injury concerns, and Leon Britton could make his first Premier League appearance since October, as he is on the bench today. "We feel confident when we play at home".
Liverpool made a mockery of them last weekend, beating them 4-1. On this evidence, with matches against Huddersfield and Southampton to come next, they will surely easily surpass that total. Of teams to have taken at least five, that is the best success rate in the competition's history (95%).
Accusations the players don't care can not be aimed at talisman Marko Arnautovic, though, after cameras caught the Austrian showing he truly cares about the club.
Antonio pulled a goal back for West Ham with 11 minutes to go. Now though, the Premier League paints a much rosier picture with Carvalhal's side up to 13th place and three clear of the danger zone. It is hard work, organisation, patience, dedication and correcting mistakes.
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