The midfielder was involved in an altercation with some travelling fans during the second half of a 2-0 defeat at Oakwell.
The result left City two points outside the play-off places with just one win in 11 Championship games.
Marshall told the club website: "In the heat of the game, I lost my composure and reacted in a way that was unacceptable, which I truly regret.
"I let myself, my team mates and the supporters down and unreservedly apologise for any offence I may have caused.
"We've set high standards as a squad this season and we share the frustrations of the fans that, as a team, we haven't performed as well as we should have in recent weeks.
"We're working hard to put that right in our last six games, starting at Brighton on Saturday, but I realise that we have to stick together as a club to make it happen - players, staff and supporters.
"The fans have been amazing this season, both at home and away, and we're going to need them over the coming games so I hope they stay behind us."