The Potters' first-half dominance was reflected in centre-back Robert Huth's eighth goal of the season but Frederic Piquionne's clear handball was missed by referee Mike Jones as the striker went on to score.
When former Hammer Matt Etherington missed a penalty seconds after the interval it seemed it was not to be Stoke's day, but Danny Higginbotham drilled a free-kick through the wall and goalkeeper Robert Green could only push it onto a post and into the net.
Pulis, grateful to be able to sweep aside any criticism of the match officials, said: "We have been very unfortunate this year, we have copped quite a few (bad decisions) in the league.
"We were very good for 25 minutes and then when they get their first shot on goal from that it was disappointing. From where I was standing it looked a stone-banker handball."
He added: "For two and a half years at this club, since we were promoted, we have been written off. We have got to three quarter-finals of cup competitions now we have a semi-final. We've finished 12th and 11th in the Premier League and the players and chairman deserve a hell of a lot of credit."
Source: PA
Source: PA