The manager was angry with Mike Dean's decision to award West Brom a late penalty, which Jay Rodriguez scored to deny the Gunners all three points.
"He was also fined 40,000 pounds".
Part of his anger stemmed from a penalty the away side won when Eden Hazard was deemed to have been fouled by Hector Bellerin by referee Anthony Taylor - a decision branded "farcical".
Wenger appeared to suggest after the Chelsea game that there may be a conspiracy against his team.
However, that ban could yet be extended if the FA decide to extend the charge in the wake of his comments both before and after Wednesday's 2-2 draw against Chelsea.
Wenger told reporters when quizzed on his outburst: "I've nothing to add, I maintain what I said. I want to be the boss". One hundred per cent [he dived].
"From what I've heard and seen in tunnels and dressing rooms down the years, I'm surprised and shocked to be charged", he said. "I have a right to have my opinion and I respect everybody's opinion". Nothing has changed. I've been in England for 21 years and I've tried to serve this game with honesty, integrity and when I have something to say, I say it.
"You have your opinion and I have my opinion and I've been in the game long enough to know that everybody can have a different opinion".