West Ham co-owner David Gold was involved in a confrontation with a group of fans after their 4-1 defeat at Swansea on Saturday.
The incident, which was recorded and has gone viral on social media, happened after Gold stopped his car to speak with travelling Hammers supporters outside the Liberty Stadium.
The group of fans repeatedly swore at Gold after seeing their side drop below Swansea on goal difference to 14th in the Premier League table following the defeat.
"I'm 82 years old," Gold said after getting out of his Rolls-Royce. "You don't understand. I'm hurting as much as you. I know it's terrible."
But furious fans hurled abuse at the co-chairman - who said he had left the game in south Wales early for "security reasons" - and urged him to leave the club.
Gold and fellow co-chairman David Sullivan have come under increasing criticism this season from fans, although some leapt to the defence of Gold after the confrontation.
West Ham's defeat was their third in four Premier League matches and has left them three points above the relegation zone.