Henry was seen gesticulating at a supporter following the 3-2 loss at the Liberty Stadium.
"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.
"So I would like to first and foremost apologise for using inappropriate language to that particular 'supporter'. I didn't intend to be malicious or threatening and am aware that it could have been said in a calmer manner."