Stoke manager Tony Pulis said his side's lack of goals is becoming a major concern to him.
There were few clear-cut chances throughout the contest and Stoke substitute bKenwyne Jones passed a good one up in stoppage time when he fired at Ben Foster.
Stoke have claimed just five points from their last 10 league fixtures and Pulis, hopeful of a strong finish to the campaign, is eager to see an improved conversion rate from his team.
Asked if he was worried about the side's lack of goals, Pulis said: "Yes, very much so. The final third at times has been the problem, but it is something we have to get on with. We got into some fantastic positions today and that final ball, or the movement, didn't lead to the goal we need. That was disappointing.
"I thought it was a very competitive game without many chances in it. At the end Kenwyne has probably had the best chance of the game and unfortunately for us, he has ended up hitting it straight at Foster. When things are going for you, that would have nestled in the corner.
"But it has got us off 33 points, which has been a millstone around our neck - and fingers crossed, now in our last eight games we can push on.''
Albion boss Steve Clarke - whose team remain eighth - gave a blunt assessment of the encounter, summing it up by saying: "Poor game, good point.''
He added: "It was a game of very few chances and probably very little entertainment for the people watching. It is a good point away from home. We want to try to improve our away record and although we always like to try to win games, sometimes it is not possible.
"This is a difficult place to come and we knew it would be a tough game and one of few chances, which is how it turned out to be. The clean sheet for us is important - it is always important to defend well, especially away from home. We will take it as a good point.''