The Stoke boss suggested Oliver had stated that, upon reflection, he believed Arnautovic had in fact fairly won the ball, but with Hughes unable to challenge his fifth caution of the term with the powers-that-be, the Welshman will have to leave him out of his team to face the Hammers.
"That's something that needs to be looked at - red cards can be overturned, why can't yellows," Hughes argued. "At some point they're going to hurt you because once you've accumulated a certain amount then you're looking at suspensions, like we are after Marko's booking.
"It's unfortunate the rules don't allow you to question it when the referee acknowledges he's made a mistake.
"It was a fair tackle. I think the guys have spoken to Michael Oliver and I think he acknowledges that maybe he's made a mistake.
"It was a good tackle. I've seen what he's seen and I can understand maybe why he's thought it's a tackle from behind but it doesn't help us, that's five bookings, we can't do anything about it and he's going to be missing at the weekend."