Davies walked onto the DW Stadium pitch at the end of his side's 2-1 loss and gestured in the direction of referee Craig Pawson.
A statement on the FA website alleged Davies' "language and/or behaviour at the end of the match amounted to improper conduct".
The Forest manager largely kept his counsel in his post-match interviews but did hint he was upset by Pawson's refusal to award his side a second-half penalty when Chris Cohen tangled with Roger Espinoza.
He said: "It's up to you guys to watch the video and write what you saw.
"I'm not going to comment on whether it was or it wasn't. I know the answer to the question, but I'm not going to tell you."