Leeds pleaded guilty to the offence and were hit with a financial punishment by the governing body. The club were also warned about their future conduct.
Forest, who incurred a fine of £45,000 last season following a more serious brawl between their players and those of Derby County, received a penalty of £12,500 while the club's defender, Chris Gunter, received a three-match suspension.
Gunter stood accused of provoking the brawl at the City Ground by stamping on Leeds winger Sanchez Watt, 10 minutes from the end of a finely-balanced Championship fixture.
The left-back was subsequently charged with violent conduct by the FA and offered a standard suspension of three games.