Speaking after the game, Pardew said: "I was annoyed that it was a penalty. I lost my cool, which isn't good. It's a passionate game and sometimes those things happen."
Parkinson has until 6pm on Monday to respond to the charge.
Unlike when Sir Alex Ferguson left Manchester United, a new Arsenal head coach will not be under immediate pressure to land a premiership title.
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Gianfranco Zola's troubled reign as Birmingham manager continued with defeat to QPR on Saturday, meaning he has taken just six
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Arsene Wenger's position as Arsenal manager has come under increased scrutiny following Wednesday's Champions League thrashing at Bayern Munich.