Stephane Sessegnon nearly grabbed what would perhaps have been a deserved three points on the basis of the overall play, only for Asmir Begovic to save excellently.
The Benin international had other chances too, although Stoke were also threatening when in possession.
Clarke felt that his side would have been worth the win however, but acknowledged that the match was even for long periods.
"I think that the game was competitive, but the more clear-cut chances were ours," Clarke told Sky Sports.
"The best quality moments and the best passing movements fell to us."
Clarke's main gripe lay with a contentious decision in the second half not to award a penalty to West Brom following Charlie Adam's apparent foul on Youssouf Mulumbu.
Clarke, whose West Brom side now sit 13th in the league, was in no doubt over his opinion on the decision, but insisted that his side will reap the dividends soon enough.
"We should have had a penalty which for some reason the officials didn't give," he added.
"Obviously the officials between themselves didn't see it, but it's clear.
"Hopefully in the weeks to come we'll get some more chances in our favour."
Clarke remained positive over his side's impressive performance however, in particular their away record this season, with a win over Manchester United at Old Trafford a highlight.
The Baggies boss was also quick to praise Stoke goalkeeper Begovic, whose performance was roundly praised after keeping out numerous West Brom attempts.
Clarke said: "When you go away from home and the home goalkeeper is voted man of the match by everyone in the stadium, I think it says it all.
"We haven't lost away from home this season which is good. We head to Anfield next week which will be difficult, but there's a lot of confidence in the camp."