On his third substitute appearance in five games under the new coach, Ayew was a 79th minute introduction as the Hammers snatched a slim win at London Stadium.
The Ghanaian came on for Michail Antonio, who was one of West Ham's best men on the day.
"Michail ran himself into the ground," Moyes said on Antonio's withdrawal, as reported by his club's official website.
"Talking of hard work, Michail Antonio literally ran himself into the ground on Saturday.
"We wanted him to stay on as long as he could because we thought he was in the mood. There’s getting tired and grinding to a halt.
"He worked really hard. He works really hard in every game and is a real handful at times.
"It’s more important that with him coming back from injury, we don’t overdo it and he gets injured. I wanted to hit them on the break but then he ran out of steam.
"We got Andre Ayew on in the end and he used his experience and his abilities to help us see the game out."
Ayew has started only one game since Moyes' reign began last month.
Reports say the Ghanaian is likely to pursue a move away when the transfer window opens in January.
Swansea City, from whom he joined West Ham on a then club record £20.5 million deal in summer 2016, West Bromwich Albion and Italian side Inter Milan are said to be interested in the Black Star's services.