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 on Friday 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."