Clarke was stunned at the decision by referee Andre Marriner to give the London side a spot kick in the 94th minute, which was scored by Eden Hazard to snatch a 2-2 draw and save Mourinho from his first ever home Premier League defeat.
"I am flabbergasted at the decision. I can't believe he gave it but I can't change it," Clarke told reporters after the draw left Chelsea in fourth, four points behind leaders Arsenal who visit Manchester United on Sunday, with his side ninth.
Clarke, who played 421 games for Chelsea before serving as assistant coach under Mourinho, said his hard-working side deserved to win, having already beaten Manchester United at Old Trafford and drawn with Arsenal this season.
Asked about the kiss on the touchline from his former boss, Clarke looked embarrassed.
"I'm not really sure to be honest. I was a little bit frustrated with the decision that had just gone against us," he said. "If it was a kiss, it was a manly one."
Mourinho was generous in his praise of the Scot, who was at his side when the Portuguese coach won two English league titles in his first spell at Chelsea in 2005 and 2006.
"Stevie is a very good coach," Mourinho said. "Defensively his team is fantastically well organised and committed and compact and solid."
But Mourinho insisted the late penalty decision was the right one after Chelsea midfielder Ramires fell under a challenge in the box by West Brom defender Steven Reid.
Hazard's converted penalty took Mourinho's unbeaten home league record at Stamford Bridge to 66 matches following 60 unbeaten games in his first spell there between 2004 and 2007.
Chelsea, who lost their last league game at Newcastle United, struggled for long periods on Saturday and only scored when West Brom defender Liam Ridgewell dithered on the ball, allowing Samuel Eto'o to score just before halftime.
Errors by Chelsea's defenders and goalkeeper Petr Cech allowed West Brom's Shane Long and Stephane Sessegnon to score two second-half goals in eight minutes before the late and disputed equaliser for the west London team.
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- Manchester United
- Eden Hazard
- Andre Marriner