He was caught red handed by television camera's as they showed McCulloch punch Morgan in the eye, this 6 days after Aston Villa's Juan Pablo Angel took an elbow to him.
The Scottish midfielder will now miss crucial games against Chelsea, Manchester United and Watford.
Morgan said; "Lee was man enough to come and knock on the door, put his arm round me and apologise."
"That's enough for me. That's it. It's finished. Let's get on with it.
"We're all sportsmen. We're going to get knocks and black eyes. It is part and parcel of the game."