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.
While admitting responsibility, it is understood Southampton 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.
An FA statement read: "The FA has fined Southampton £20,000 after they admitted a charge of failing to control their players.
"The incident occurred following the awarding of a penalty to Norwich during the match at Carrow Road on Saturday 9 March."