The visitors were already trailing 2-0 to early goals from Samuel Eto'o and Andre Schuerrle when Marriner awarded a 15th-minute penalty, and sent off Kieran Gibbs after team mate Alex Oxlade-Chamberlain handled a shot from Eden Hazard on the goalline.
TV replays showed Oxlade-Chamberlain clearly mouthing "it was me" during the aftermath but the referee, who took a long time before awarding the penalty, stuck to his original decision.
"Andre is an experienced referee and is obviously disappointed that an error of mistaken identity was made in this case," the Professional Game Match Officials said in a statement.
"Incidents of mistaken identity are very rare and are often the result of a number of different technical factors," added the referees' group.
"Whilst this was a difficult decision Andre is disappointed that he failed to identify the correct player. He expressed his disappointment to Arsenal when he was made aware of the issue."
Chelsea manager Jose Mourinho, who has never lost to Wenger in 11 games, gave the officials the benefit of the doubt.
"There were lots of people in the box," he told BT Sport.
"Eden shoots, one player comes behind the keeper and dives like a keeper and touches the ball with his hand.
"From the bench you couldn't see, one of my assistants said it was (Mikel) Arteta, one said Chamberlain. The penalty is a penalty and the red card is a red card but to the wrong player."
The FA explained the course of action now open to Arsenal on its Twitter account.
"Clubs can appeal mistaken identity to the FA although the FA can pro-actively review also," it said.
"Following a red card clubs can also review possibility of a wrongful dismissal claim to the FA unless dismissal is for 2 yellow cards."
- Sports & Recreation
- Eden Hazard
- Alex Oxlade-Chamberlain
- Arsene Wenger