Saints were charged on Tuesday for the unsavoury scenes that followed referee Mark Clattenburg's decision to award a penalty for a Luke Shaw foul on Grant Holt.
Artur Boruc kept out Holt's subsequent spot-kick but Saints' players continued to protest after the 0-0 draw and were joined on the pitch by manager Mauricio Pochettino.
The club had until 4pm today to respond to the charge and Press Association Sport understands they have accepted the punishment.
It is understood that the club, while accepting the charge, highlighted to the FA that such behaviour is not a regular occurrence and that it was the first time they had faced such a charge.
Southampton also pointed to the circumstances surrounding what they felt was an unjust penalty award by referee Clattenburg.
Speaking before the charge was accepted, manager Pochettino said: "I don't really feel bad about it because I had full respect for the referee.
"I went to speak with him and perhaps I should have waited until he came to the dugout to speak to him, but I was always on speaking terms.
"That is the kind of person I am - a spontaneous person.
"I could be at fault a little bit for actually entering the field, but I must say I was on speaking terms with the referee.
"He spoke back to me and there was never anything above that. Perhaps I should have waited for him to come back to the dugout but I was defending the interests of my club and he was defending his job as well."
Southampton will want to quickly move on from the incident and have the perfect opportunity to do so when Liverpool come to St Mary's tomorrow.
The match will see Pochettino come up against highly-rated Philippe Coutinho, who he worked with at Espanyol last season.
Saints were reportedly interested in bringing in the 20-year-old midfielder during the January transfer window, only to be beaten to the signing by Liverpool.
Pochettino was coy when asked whether he had tried to lure Coutinho to the south coast, but more forthcoming when asked about the quality of the player in line to start at St Mary's tomorrow.
"What has happened in the past, happened in the past," Pochettino said. "We can't change it or do anything about it. Actually, talking about it is not going to do anything positive either.
"Philippe is a Brazilian player and, as it happens with most Brazilians, he has a special magic in his feet.
"Aside from the magic that he has, he also has an amazing work rate and that makes us doubt whether he fits the mould of a typical Brazilian player or a European one because his work ethic is outstanding.
"What is important about him is he is a good lad, a good kid - a great, humble person.
"I do think Coutinho has that same quality that Ronaldinho and [Lionel] Messi have, but he has much to prove yet.
"What is really clear to me is that Coutinho is a really responsible player - really dedicated and responsible to his own players."