The Baggies looked set for a famous victory at Stamford Bridge before referee Andre Marriner awarded a penalty deep into injury time when Ramires went down after colliding with Steven Reid.
Eden Hazard scored to earn Chelsea a 2-2 draw, leaving West Brom boss Steve Clarke furious.
Clarke told wba.co.uk: "We've had a phone call from Mike Riley to apologise.
"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."
It is the second apology West Brom have received in a month after referee Howard Webb also said sorry for not giving them a penalty during the goalless draw with Stoke.
The club have sent a letter to the Premier League and referees' body Professional Game Match Officials Limited highlighting four penalty decisions that have gone against them in the opening 11 games of the Barclays Premier League season.
"The purpose of the letter is to try and provoke discussion," said 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.
"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."
West Brom sit 10th in the table ahead of the derby clash with Aston Villa on Monday.
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- Andre Marriner
- The Baggies