The former Swansea star and record Hammers signing has made just a dozen PL appearances for the club since arriving from Wales.
And Bilic was in no mood to plunge him into the action against the Baggies so soon after his return from the African Cup of Nations.
He said: “Andre Ayew came back on Friday. He had a long Africa Cup of Nations – they didn’t play more games than we played here so it’s not physical, but psychologically it means a lot to them and it drained him.
“They were there until the end – they played for third place – so we gave him a few days off and he came back on Friday. That’s why he was not in the squad on Saturday.”