Pochettino has until Friday to respond to the charge. A ban would be likely only if Pochettino is found to have used abusive or insulting language. It would be the first time Pochettino has been banned or fined during his managerial career in England, which started at Southampton in 2013. He did, however, become the first Premier League manager to be warned for his touchline behaviour under new regulations introduced by the FA.
Pochettino hinted after the game at Turf Moor that he would accept the FA's decision if the governing body decided to launch disciplinary action.
"I will accept everything that can happen from the Football Association but I hope they won't go any further," he said.
The Tottenham manager had complained about the corner awarded from which All Whites striker Chris Wood headed in Burnley's opening goal, and was unhappy about several decisions that went against his side.
The Argentine began the angry exchange with Dean after walking on to the pitch at the final whistle. He appeared then to walk away from the referee before turning around furiously and storming back towards him.
He was joined by Perez, who jabbed a finger towards Dean's face, with both Spurs coaches appearing to have been angered by a comment made by the referee. Pochettino could be heard telling Dean to "repeat it on camera".