Spurs interim manager Cristian Stellini and Brighton coach Roberto De Zerbi were sent off in the 58th minute after a fracas involving both benches.
“Both clubs admitted they failed to ensure that their benches conducted themselves in an orderly fashion and did not behave in a way which is improper during the 58th minute,” the FA said in a statement.
Speaking after the game, De Zerbi praised his players for their performance, before criticising Tottenham for allegedly trying to influence the referee.
‘We are very disappointed, very frustrated with the result. We have to be proud of this performance,’ he said.
“We are not to forget we are Brighton. We deserved to win the game. We improved because we show our quality and our style of play.
‘I don’t want to put more pressure on the referees. I don’t like to discuss them.
‘There were a lot of situations very clear. You can take your opinion about this. My work is to give my players a clear idea of play.’
However, Stelllini, seemingly intent on drawing a line under the incident, admitted recently that the FA had been right to charge the two clubs.
‘Maybe for the atmosphere we created it is good the (FA) decision,’ he said. ‘We have to be better but personally I am happy we showed we are a team, we are linked, we are close and we defend ourselves and our club.
‘At the same time I am happy because I feel I was not involved in anything, so it is a good decision I stay on the touchline tomorrow.’