Fulham vice chairman Tony Khan told a fan to "go to hell" in a tweet after the 2-1 loss to Burnley left the London club with only one win in nine English Premier League games on Saturday.
Burnley profited from two own-goals in quick succession to come from behind and leave Fulham five points from safety.
Khan tried to assuage concerns of fans by promising "multiple signings to improve the squad" in the January transfer window while stressing on Twitter: "It's on our players now to fight, finish & win."
The son of American owner Shad Khan reacted angrily to a supporter responding: "Leave my club please."
Tony Khan, who is director of football operations at Fulham, replied : "Never. I'll die at this club. Go to hell."