The French tactician received his marching orders with seconds to go in his side's 2-1 defeat to Manchester United after he kicked an empty water bottle down the touchline following a disallowed goal.
He was sent to the stands by referee Mike Dean on the advice of fourth official Lee Probert but confusion then reigned as Wenger seemed unaware of where he was supposed to go.
He at first moved to the back of the Arsenal dugout then started to walk down the touchline as the whistle was blown.
League Managers Association chief executive Richard Bevan says Wenger will now receive an apology from the Premier Game Match Officials Board which appoints officials to top-flight games in England.
On the decision to penalise Wenger, Bevan said: "Although correct in 'law', it was completely out of context in the game and it was followed by the nonsense which followed over where Arsene Wenger should sit."
He added: "I've spoken to (Premier League referees chief) Keith Hackett and he fully recognises the situation was an error and an apology will follow to Arsene Wenger.
"Lee Probert totally failed to manage the situation and created a needless pressure point taking the focus away from the pitch in a big event with only a minute to go."
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