Players and coaches from both sides were involved in the brawl
Derby and Nottingham Forest have been fined £35,000 each by the Football Association for failing to control their players at Pride Park last month.
The brawl broke out at the end of Derby's 1-0 win on 30 January.
Each side will also pay £10,000, which was suspended from another skirmish between the East Midlands rivals earlier in the season.
Players and coaching staff from both sides scuffled after an initial clash between Jay McEveley and Chris Gunter.
Forest boss Billy Davies refused to shake hands with Rams counterpart Clough at full-time.
After the incident, Davies lodged a complaint with the FA and the League Managers Association against Clough.
Davies says Clough kneed him in the back of the leg, but the Derby boss insisted: "It was purely accidental."
"The matter is now in the hands of my lawyers, who are dealing with that," added Forest boss Davies.
Clough plays down 'accidental' clash with Davies
Derby won the game 1-0 after a late header from Rob Hulse.
Davies is a former Derby manager and took the club to the Premier League in 2007 - and he continued: "I have great memories of Derby County and great friends at the club still.
"If the three points helps them avoid relegation then I am delighted for them.
"We did not perform on the day in the way we can because we got caught up in the stop-start nonsense of the rivalry between Forest and Derby."
Earlier this season both sides were fined following a skirmish, Forest £25,000 and Derby £20,000, with £10,000 each of the fines suspended.
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