The Blue, Black and Whites had England wing Anthony Watson sent off for foul play after half-time in the 30-10 loss.
"Passions were high last night but it's not acceptable for rugby or for Bath," managing director Tarquin McDonald told BBC Radio Bristol.
"Clearly we're looking into it and we'll deal with it appropriately."
Bath, who are ninth in the table having reached the Premiership final last May, released a statement on Saturday confirming they were "investigating the incident and will ensure appropriate action is taken".
Bath will investigate reports that a supporter entered the referee's room to confront the match officials after Friday's defeat by Saracens at The Rec.