Gillespie's dismissal sparked ugly touchlines scenes
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The Football Association has fined Sheffield United £10,000 and Reading £5,000 after a touchline fracas during their match on 20 January.
Reading coach Wally Downes has also been fined £2,000 and handed a one-match touchline ban.
Downes had admitted a charge of improper conduct.
That match also saw Blades substitute Keith Gillespie sent off for swinging an arm into the face of Reading midfielder Stephen Hunt.
The incident was followed by the altercation between Blades boss Warnock and Downes who were both, consequently, sent to the stands.
Downes was seen to confront Warnock, seemingly for a kicking gesture made by the Blades boss, sparking a brief brawl involving substitutes and backroom staff from both sides.
Warnock's said after the incident that his gesture was made in order to tell referee Mark Halsey that an earlier tackle by Reading's Steve Sidwell on Blades defender Chris Armstrong had been the worst of the game.
According to Coppell, Downes thought the United boss had instructed his players to kick their opponents.
A charge of improper conduct against Reading academy manager Eamonn Dolan was withdrawn.
Reading won the fixture at the Madejski Stadium 3-1.