Last weekend Edin Dzeko struck in stoppage time to give Manchester City all three points at the expense of the Baggies, while today Papiss Cisse found the net with a few seconds remaining to give Newcastle United a 2-1 victory.
"I certainly didn't think it would be a game we were going to lose. I thought we had good control in the first half and created good chances," said Clarke.
"I felt we were unfortunate to be behind at half-time. It was a horrible moment, a big deflection in injury time and it's in the back of the net.
"After the late goals we conceded last week [in the defeat by Manchester City], it's hard to take."
Clarke's team are currently eighth in the Premier League table.