Forest boss Billy Davies accused his opposite number Nigel Clough of deliberately kneeing him in the back of the leg following a stoppage-time melee involving players and staff from both clubs.
The reverse fixture at the City Ground in August also ended amid scenes of mass confrontation.
A Football Association Commission Statement read: "At an Independent Regulatory Commission earlier today both Derby County and Nottingham Forest were fined for failing to control their players.
"Both clubs accepted the charge following an incident of mass confrontation in the fixture at Pride Park on 30 January 2010.
"The clubs were fined £35,000 and warned as to their future conduct, whilst a further £10,000 suspended penalty imposed on the clubs from a case earlier in the season was also activated."