Hammers striker Andy Carroll opened the scoring in the fifth minute of Barclays Premier League contest with his first goal of the season, rising above Peter Crouch and crashing a header past Asmir Begovic, who had rushed off his line to try to punch the ball away.
The hosts equalised in the 32nd minute when Crouch, following up his own header that had hit the bar, saw his acrobatic effort go in off the shoulder of Peter Odemwingie.
Kevin Nolan thought he had made it 2-1 to the visitors when he put the ball in the net in the 61st minute but the effort was ruled out for offside.
Stoke subsequently went on to wrap up victory, with Marko Arnautovic getting through a crowd of players and slotting in on 69 minutes before Odemwingie finished a Potters counter-attack by lashing home with 11 minutes to go.
West Ham boss Sam Allardyce felt Pawson missed a "blatant" handball by Muniesa in the home box shortly after Arnautovic had made it 2-1.
But Hughes felt differently about the Muniesa incident.
"I think there was contact but in fairness to Marc Muniesa I think he wasn't even looking at the ball when it actually hit him," Hughes said.
"He made a genuine attempt to challenge for the ball and was up against Andy Carroll, who is about a foot and a half bigger than him, so you have to use your arms for leverage to try to get anywhere near a challenge that will put him off.
"It probably did hit his elbow, but it wasn't deliberate and it would have been harsh if it had been given - and even it had been, I still think we had enough to take the game away from them."
- Sports & Recreation
- Peter Crouch
- Andy Carroll
- Peter Odemwingie
- Marko Arnautovic
- Asmir Begovic
- Barclays Premier League