Mourinho was on the verge of his first ever Premier League defeat at Stamford Bridge after Stephane Sessegnon and Shane Long had put the visitors 2-1 up following Samuel Eto'o's first-half opener.
Chelsea's attempts to get back into the game were thwarted by a stubborn West Brom defence but, in the 94th minute, Ramires fell after contact with Steven Reid and referee Marriner awarded the spot kick.
After protests from the visitors, Eden Hazard converted from 12 yards to secure a point, but Mourinho was adamant the official had made the right call.
"Yes, I think it was a penalty, I'm sure it was a penalty," he said.
"I watched in the screen after the match without any pressure or tension, I watch it and I watch it, from different angles, and different speeds and it is a clear penalty.
"And no doubt that is a free-kick against West Brom when they scored the second goal so if someone has to be upset with the referee's work that's Chelsea and not West Brom.
"I just know that it's hard when you think you are winning the game and you get a penalty in the last minute it's hard to accept but clearly if somebody has the right to be upset it's us.
"But the referee is a top one, one of the best in the country, one of the best in Europe. Today I didn’t like his performance, he made too many mistakes all of them against us, but Andre is one of the best referees."
