Davies claims he was kneed in the back of the leg by Clough in a melee on the pitch in the dying moments of Derby's 1-0 win at Pride Park. The Forest chief refused to shake hands with Clough at full-time and insists the Rams boss intentionally sought to hit him.
The Football Association have confirmed they are investigating the mass melee. Officials are studying the referee's report and video evidence before deciding on any charges.
An FA spokesman said: "We are investigating the events at Pride Park."
Davies told Sky Sports: "I'll tell you what happened and you can ask Nigel Clough this, because I said to him that he was out of order when I was in the middle [of the skirmish].
"He came in and kneed me in the back of the leg. I said to him that I wouldn't have minded him doing it to my face but to do it to my back was a bit cowardly and that's why I never shook his hand at the end.
"He tried to claim it was an accident but he knows as well as I know that it wasn't an accident.
"I have no doubt in my mind over what happened, hence why I never shook his hand."