Yoan Gouffran put the hosts ahead nine minutes before the break but Clarke's men drew level courtesy of Chris Brunt's 53rd-minute strike.
West Brom were on equal terms for just four minutes, with Moussa Sissoko's long-range effort handing Newcastle all three points.
Clarke's men have now won just one of their last seven matches but the Scot took heart from his side's performance after the interval.
"We were passive in the first half and didn't create enough," he said.
"Both teams were cancelling each other out and their goal came out of the blue.
"It's always disappointing to concede a cheap goal from a set-play (and) I think we were feeling a little sorry for ourselves at half-time
"The reaction was good (in the) second half and we got ourselves back in the game. A wonder strike has denied us any points."
West Brom sit 12th in the Premier League ahead of a home game against Manchester City on Wednesday.
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