The League Two side were comfortable winners over Forest, who were reduced to 10 men.
Megson said: "Chester played well but we were an embarrassment.
"I am not going to turn round and say which individuals did well or not. The responsibility rests at my door, but I do not think anyone on that pitch can say they played well.
"The effort and commitment are not there away from home. We had people missing for various reasons, but those who came in did not take their chance."