The Baggies made a fairly lively start to the game, with skipper Chris Brunt shooting at Asmir Begovic in the fifth minute.
Stoke then shaded it for the rest of the first half but only really went anywhere close to breaking the deadlock through a deflected Jon Walters shot.
Potters frontman Peter Crouch and his opposite number Romelu Lukaku failed to finish with headers as a slightly-improved second half got under way before Kenwyne Jones wasted his opportunity at the death having chested the ball down in the box.
Clarke - whose team remain eighth - 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."