Marshall, 21, was involved in a verbal exchange with a small number of the 2,000 travelling supporters during the second half of Monday's 2-0 loss at Oakwell.
The player told the club's official 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."
Leicester have taken just two points from the last 21 available to go from automatic promotion contenders to battling to earn a place in the play-offs.
They will go into the game against Brighton, who currently occupy the final play-off spot, two points behind the Seagulls.
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