And opposite number Mark Hughes conceded the Baggies were unfortunate after Charlie Adam escaped punishment for tripping the visitors' Youssouf Mulumbu.
The controversial second-half incident was one of few moments of interest in largely dull Barclays Premier League contest at the Britannia Stadium.
Clarke said: "I think the two words for it are stonewall penalty.
"How the officials have missed it is beyond belief, but sometimes you get decisions and sometimes you don't. It is a decision that didn't come our way."
Adam appeared to clip the heel of Mulumbu in the area 10 minutes after the break but referee Howard Webb, after looking to his assistant for help, was unmoved.
Clarke said: "If he had wanted to con the referee he would have gone down on the first contact.
"He managed to wriggle free of that. It is clear, whatever angle you look at it, it was a penalty.
"I don't think he meant to do it but he ran down the back of his foot. It was a clear penalty.
"I don't criticise the referee overall. You have to understand I am talking about one decision here where I find it difficult that between them they didn't see the penalty."
The Baggies' Stephane Sessegnon was twice denied by the excellent Asmir Begovic, including in the last minute after a mazy run through the Stoke defence when he probably should have scored.
Stoke's best chance was missed by Stephen Ireland, blazing over on the counter-attack, while quick-thinking Adam also forced Boaz Myhill to save with a spectacular effort from the halfway line.
Hughes said: "We are grateful to Asmir at the end. That is an outstanding save.
"Given the time of the chance, if they had scored then they would probably have taken the game away from us.
"They will feel a bit aggrieved with the penalty claim they had - it looked like it was a penalty.
"But we had similar complaints a couple of weeks back at Fulham. As the old adage goes, they even themselves out. Apparently."
Stoke have scored just four times in the league this season and Hughes is growing concerned, even though he remains happy with the number of chances they are creating.
He said: "We are struggling for goals but that was prevalent before I came here.
"It is something we are working on. In terms of chances we are still creating the same, if not more, given we are playing in a slightly different way.
"It is up to us to make sure we convert the ones we get.
"We had a number of chances here, a number of balls flashing across the six-yard box, just needing a touch to convert them, and Stephen Ireland had a great opportunity.
"They had a number of chances in the first half when we were a little bit passive in our work but, apart from the one at the death, they didn't create that many more."
Clarke felt it was his team that had the better opportunities.
He said: "We had some terrific chances. We had three clear-cut chances, two for Stephane and one for Morgan.
"With better finishing and maybe a lesser goalkeeper, on another day, we should be talking about a good victory. Instead it is a hard-earned point."