Arsenal boss Arsene Wenger believes Costa deserved to be sent off for bumping the chest of Laurent Koscielny and raising his hands to the Frenchman's face at Stamford Bridge.
But the controversial striker got away with only a yellow before Gunners defender Gabriel Paulista saw red for retaliation.
And Mourinho has jumped to the defence of the 26-year-old, insisting opponents are 'stupid' for allowing him to wind them up.
The Blues boss said: "The players are tired of hearing me talk about emotional control. They had emotional control.
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Jose Mourinho backs Diego Costa following Gabriel Paulista clash
"Arsenal didn’t have emotional control. When you don’t have it you are punished. We did well, they did not.
"If he [Diego Costa] winds players up it is because the others are stupid."
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