The Baggies boss has said he rues the lost points that his club will never get back despite receiving sympathy following the draw against the Blues
Andre Marriner saw fit to award the Blues a spot-kick deep into second-half stoppage time of the November 9 contest, with Eden Hazard converting from 12 yards to draw level at 2-2 and deny the Baggies victory.
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"We've had a phone call from Mike Riley to apologise," he told West Brom's official website. "It doesn't get us any more points but it's nice of Mike to phone.
"If he's apologising, he obviously feels it was the wrong decision. We have to put it behind us now and move forward."
Clarke also clarified the purpose of a letter sent by his club to the Premier League and Riley condemning referees' decisions in the Baggies' previous encounters with Southampton, Arsenal and Stoke, in addition to the Stamford Bridge incident.
"The purpose of the letter is to try and provoke discussion," he continued.
"It's not necessarily a discussion between us and the authorities, but a discussion between everyone and the authorities to see if there is a way we can improve the game.
"That's my understanding of the basis of the letter - it's no more than that.
"If there is technology that can be used to help referees make difficult decisions, which is what they have to do, then let's look at it and see what we can come up with.
"If we can improve it, good, if we can't improve it then we'll stick with what we've got. But let's talk about it."