The Rams forward appeared to stamp on the calf of the Liverpool defender during their 6-0 thrashing at Anfield in a touchline incident that was missed by match referee Alan Wiley.
However, Derby have backed their player after releasing a statement denying the charge.
"Derby County have denied a Football Association charge of violent conduct levelled at Craig Fagan," read the statement.
"The 24-year-old was informed on Tuesday of the FA's decision to issue the charge following an incident involving Liverpool's Alvaro Arbeloa during Saturday's defeat at Anfield.
"Fagan's case will now be heard by a regulatory commission on Thursday."