The Gunners players were applauding the travelling support after the disappointing 3-2 loss when Henry clashed with the fan in question.
Henry came forward last night and revealed his regret at the incident but insisted the fan was not helping their cause with abuse.
“I was really shocked and disappointed on Sunday — and not just at the result,” Henry told The Sun.
“After the final whistle of a very tricky game, I insisted the whole team go and applaud the Arsenal supporters.
“When I arrived in front of our own fans, I couldn't understand the abuse the team were getting from one of them.
“I wanted to tell the fan in question that we need their support not abuse. The sentiment was right but in hindsight could have been better expressed.”
A Danny Graham goal, immediately after a Theo Walcott equaliser, sealed the win for Swansea at the Liberty Stadium.
It was the sixth away loss of the season for Arsene Wenger’s side and also confirmed no other team in the division had conceded as many goals on their travels.
Henry accepted there was bound to be frustration at the manner of their losses, but insisted the fans need to realise how much effect abuse can have on the team.
“So I would like to first and foremost apologise for using inappropriate language to that particular 'supporter',” he added.
“I didn't intend to be malicious or threatening and am aware that it could have been said in a calmer manner.
“We have had great moments at this club but we are all in this together. We need your support in the good times but more importantly the bad.
“Let's get behind the team against Manchester United on Sunday and try to get three points to get the season back on track.”