The Portuguese was furious with Taylor after he booked Chelsea midfielder Cesc Fabregas for diving in the Dec. 28 match.
Mourinho said the referee's failure to award a penalty was a scandal and that he should be ashamed.
He added that his team were being unfairly targeted in a campaign waged against them after Fabregas became the fifth Chelsea player to become involved in a row over diving in a matter of weeks.
The Spaniard, though, appeared to be tripped by Southampton defender Matt Targett in the penalty area.
"In other countries where I have worked, tomorrow in the sports papers it would be a front-page scandal because it is a scandal," said Mourinho.
"It is not a small penalty, it is a penalty like Big Ben. In this country, and I am happy with that, more than happy with that, we will just say that it was a big mistake with a big influence on the result.
"I will go to the referee and wish him a good year and tell him he will be ashamed," added Mourinho.
In a statement, the FA said his remarks constituted improper conduct in that they allege and/or imply bias on the part of a referee or referees and/or bring the game into disrepute.
Mourinho has until 1800 GMT on Jan. 13 to respond to the charge.
The FA will not take any action against him following the comments he made before the game against Stoke City on Dec. 19 but gave him a formal warning as managers and players are banned from making pre-match media comments about officials.
Before the game Mourinho said he hoped referee Neil Swarbrick "does his job".
"I like these matches," added the Chelsea manager. "It's no problem with a good referee that can understand what is aggressivity or when aggressivity finishes and when the rules of the game start.
"I know it is difficult for every team to play this kind of match but again I'm not worried. The referee is there exactly to judge what is aggressivity. And aggressivity I always welcome, it makes the game much more beautiful and difficult."
(Editing by Tony Jimenez)
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