The Baggies created very little until forced to chase the game - their best chances saw Gareth McAuley denied by Gary Medel's clearance on the line and David Marshall save superbly from Shane Long's header with four minutes to go.
"We created some chances as we normally do," said manager Clarke. "At the moment things aren't quite going for us.
"I don't think it's a lack of confidence. We tried to pass the ball but Cardiff started brightly and put us on the back foot.
"We resisted them and stayed in the game. The longer the game went on, the more we played and the more chances we created. It's difficult."
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball