Brown Ideye scored the game's only goal after 19 minutes as West Brom went on to beat Pulis' former employers, but the hosts were left somewhat frustrated with the referee's performance.
Nigeria international Ideye could have had a second 10 minutes before the break, but he was controversially denied by the offside flag, before Stoke luckily avoided conceding a penalty towards the end.
Craig Dawson was sent tumbling by substitute Geoff Cameron with 14 minutes to go and Oliver rejected the hosts' appeals.
Pulis had no doubt about that incident and was amazed at the decision not to give a penalty, even if it ultimately mattered little.
"There was the offside incident which I'm not sure about but the one for the penalty was poor," he said.
"Michael will look at that and be very disappointed. That was as blatant a penalty I've seen for a long, long time.
"As for the other one [the offside], I thought [Stoke goalkeeper Asmir] Begovic touched the ball and, from what they tell me, the lad should be onside again as it is back in play."
Pulis also focused on Darren Fletcher, lauding the Scot's impact since his January arrival from Manchester United, as the experienced midfielder impressed once again on Saturday.
"He has been a fantastic signing," Pulis added. "He's a tremendous lad, his enthusiasm and energy levels are top class.
"He looks as sprightly as any 20-year-old. He and [James] Morrison dominated the midfield.
"They've played together for Scotland and a lot of good stuff came from those two."
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