Pulis, whose team have now won three matches in a row, was concerned after they had struggled to impose themselves on proceedings in the opening period, but penalties from Matthew Etherington and Jon Walters, who later fired his second, sealed Stoke's second away win in the league.
"I thought West Brom played their part in the game," said Pulis.
"It was a pretty open game in the first half and they moved the ball around quickly.
"The good thing for us was that they never had that many clear-cut chances, but I was a little bit disappointed and we had a little bit of a go at them at half-time.
"Then they have come out and just stepped it up a bit, which it what we needed to do."
Source: PA
Source: PA