Malky Mackay's charges earned a first win in six attempts in the Premier League at the Cardiff City Stadium on Saturday as Peter Whittingham's superb header after 65 minutes beat Boaz Myhill in the West Brom goal.
But the visitors felt aggrieved not to be given a spot-kick shortly after when Shane Long was bundled over in the area by Ben Turner, with referee Webb waving away the protests.
Long is convinced that Webb should have pointed to the spot, but Clarke opted not to criticise the decision.
"Shane said he thought it was a penalty," he said. "Unfortunately for us Howard Webb didn't think it was a penalty.
"What else can I do? After the game what can I do? I can rant and rave and criticise referees but it's not my style."
The loss was West Brom's fourth in a row in the Premier League and their sixth without a victory.
But Clarke believes his side were unlucky to come out on the losing side of a tight encounter.
He added: "The game I thought was quite an even game, there wasn't much in it.
"The first goal was always crucial. Unfortunately it went to Cardiff. It went to Cardiff in a moment when it looked like neither team would score, it looked it would finish 0-0.
"The reaction from the players was good, we created some chances as we normally do but at the moment things aren't going for us."
