Maurizio Sarri has been fined £8,000 by the Football Association after admitting a misconduct charge relating to his dismissal during the closing stages of Chelsea's 2-2 draw with Burnley.
Sarri was dismissed by referee Kevin Friend and fourth official Roger East in the 94th minute of Monday's match, which was marred by several angry exchanges between the two benches and the match officials, culminating in a mass brawl in front of the dugout at full-time.
Chelsea passed details of what was said by Burnley employees to Sarri onto Friend, who was expected to include it in his report of the game. But in subsequent statements, both clubs indicated their desire to move on from the incident.
"Issues arising between both benches during Monday night's match have been resolved between the coaches and clubs, and a line has been drawn under the matter," a joint statement issued by both clubs read.
Emotions between the benches flared early in the game, with Dyche's assistant Ian Woan pointing out that Sarri was encroaching on the visiting technical area while Chelsea took issue with what they perceived as Burnley time-wasting.
Tensions escalated as Burnley stubbornly repelled waves of Chelsea pressure and acted to slow the game down in the closing minutes, and at the final whistle staff from both clubs converged at the entrance to the Stamford Bridge tunnel.
Burnley goalkeeping coach Billy Mercer had to be restrained after becoming incensed with Chelsea counterpart Massimo Nenci and fitness coach Paolo Bertelli, while defender Antonio Rudiger also waded into the melee despite nursing an injured knee.