Steve Clarke's men led 2-1 at Stamford Bridge but were harshly penalised in stoppage time by Andre Marriner after an innocuous collision between Ramires and Steven Reid, allowing Eden Hazard to score from the spot.
Riley has since deemed it appropriate to send his apologies to West Brom in an apparent admission that the official made the wrong call on the day.
"We’ve had a phone call from Mike Riley to apologise," Clarke told the club'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."
The Hawthorns club have also sent a letter to the Premier League and Professional Game Match Officials Limited in the hope of prompting debate over new ways to help referees make difficult decisions.
"The purpose of the letter is to try and provoke discussion," continued Clarke.
"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."
West Brom next face a West Midlands derby against Aston Villa on Monday.
