Having thrashed Stoke 3-0 in the Premiership only a week ago, hope were high that the Hammers could progress to the semi-finals of the competition.
The Hammers were undone by some typical route-one football from Stoke and some dodgy decisions in a hard fought contest.
Robert Huth scored the opener for Stoke from a Rory Delap long throw before Frederic Piquionne scored the equaliser in which he appeared to handle the ball.
A Danny Higginbotham strike from a free-kick was enough for Stoke to seal a place in the semi-final against Bolton.