West Ham ended Villa's winning run with a 2-1 victory as their hopes of qualifying for Champions League football were kept alive thanks to goals from Andriy Yarmolenko and Pablo Fornals in the second half.
Moyes admitted after the game that containing Brazil international Philippe Coutinho was the key behind his team's success.
"He's a top player and he's shown that in the last month or so," Moyes said.
"Villa came into this in great form and the front three especially.
"It was a tough game for us because we knew they had their tails up and we had to find a way through.
"I thought we played quite well in the first half.
"In the second half, I'm not sure if Villa got better or if we dropped off with the injuries.
"It made me think, 'My goodness, this is seeping into us a wee bit, the midweek stuff, but in the end we rallied, got a couple of goals which we haven't done recently and I thought we looked quite comfortable at 2-0 but made it nervy at the end."
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