The Blues were given the spot-kick when Ramires went down under a weak challenge from Steven Reid, before Eden Hazard converted the last-minute equaliser, and Clarke stated his disbelief at the outcome.
"I'm flabbergasted at the decision, I can't believe he gave it," Clarke is quoted as saying in the Daily Mail.
"I saw it at the time. I've been in the game a long time and I knew he was already on the way down before anyone was near him. The referee has to be 100% sure. How he can be 100% sure is beyond me. It was not the correct decision.
"It's the kind of penalty that can be given when you've got a home crowd shouting for everyone. Refs are only human and can make mistakes."
The draw at Stamford Bridge leaves West Brom ninth in the Premier League.