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."
Responding to criticism over the tone of his tweet, Khan complained the fan was among those who "give no credit when things go well."
Khan expanded further in response to an Associated Press tweet posting an article on the exchange.
"This wasn't my 1st twitter interaction with this fan," Khan said. "When times are down, he's on me, but even less than 2 weeks after promotion he complained at me. Thanks to our fans that stand by the club. Come on Fulham."
But Fulham might be making an instant return to the second tier after this latest setback.
Andre Schurrle's early opener for Fulham was cancelled out in the 20th minute when Jeff Hendrick's effort went in off Joe Bryan.
Three minutes later, Denis Odoi inadvertently beat Sergio Rico, heading in after Hendrick crossed.
Calum Chambers headed against the Burnley bar soon after and Fulham substitute Luciano Vietto was denied after the break by James Tarkowski and Tom Heaton — two players hoping to impress England boss Gareth Southgate, who was watching from the stands.
Burnley held on to record a third consecutive league victory, further easing its relegation fears.
Fulham remained second to last.