Goals from Gary Hooper and Leroy Fer helped the Canaries earn a valuable win at The Hawthorns as they leapfrogged their opponents into 14th position in the table.
It is now one win in nine games for the Baggies, who drop to within two points of the relegation zone.
"We created a lot of chances but we did not get the goal. We made it difficult for ourselves conceding the goal which came from a throw-in and was a soft goal," said Clarke.
"It gave Norwich something to hang on to. We created enough chances but could not get the goal that would change the game in our favour."
Clarke also refused to blame Stephane Sessegnon for his misses or criticise referee Mark Clattenburg for failing to spot an apparent handball by Martin Olsson.
"The one chance was going in the net, it hit Martin Olsson on the hand which stopped it going in," he said.
"Whether the referee saw it or not does not help us. I am not sat here crying about a penalty decision because it's a tough one to call but the ball was going in the net, so it's hard to say it was a miss."