Chelsea avoided defeat with a late goal from the spot in the 2-2 draw between the two sides at Stamford Bridge prior to the international break after referee Andre Marriner ruled that Steven Reid had unfairly bundled over Ramires following an innocuous collision.
Riley, the general manager of the Premier League and Professional Game Match Officials Limited, has since contacted West Brom boss Steve Clarke to say sorry for the penalty award.
While Mourinho insists Marriner's decision was correct, the Chelsea manager questioned why the apology had been made, as well as whether any more had been issued to other managers.
"I'm really interested to read and listen to comments the media make about that situation," he said.
"If they (referees) do that (apologise) in my career, my telephone would be very busy.
"I'm curious to know if Steve Bruce, Chris Hughton, (Michael) Laudrup got a call. Nobody called me to apologise about the fact that there was not a free-kick against West Brom for their second goal. Nobody apologised about the (lack of a) penalty against Everton.
"I'm curious to know if it is just an isolated phone call and if people see that as a normal situation. If now on it is going to be the same for everybody.
"If a controversial decision, hypothetically, favours Chelsea, they (referees) know they are going to be publically exposed by their boss."
Chelsea will welcome back defender Ashley Cole following his rib injury for Saturday's London derby against West Ham at Upton Park, although striker Fernando Torres (thigh) remains ruled out.
Having won once on the road in the Premier League this season, Mourinho is eager to break down what he feels is likely to be a defensive West Ham side.
"I have the feeling that many teams in the Premier League are playing very defensive football," he continued.
"Trying to stop the opponent playing and after that seeing what will happen. That is giving good results to different teams against those considered better teams.
"Nobody is really dominant in this league. I'm expecting a very difficult match.
"Of course we want to do better (away from home). We need to get more points in the next five matches away than we did in the first."
