Carragher wrote in the Daily Mail: "If Manchester United think sacking David Moyes is the key to bringing them future harmony, they should think again.
"They are in the real world now, just like everyone else. The problems to which they were immune while Sir Alex Ferguson was in charge are going to surface. Getting rid of David Moyes will not suddenly transform their position.
"It is sad to see Moyes go. He is a good man who had great pride in being given the responsibility to lead United and it was far from ideal that his departure from Old Trafford was played out so publicly."
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