The 34-year-old has re-joined the Gunners on loan from the New York Red Bulls and came off the bench during the 3-2 loss.
And the Frenchman was spotted having a heated exchange with one fan and making gestures before storming off the pitch after the match.
A Gunners source said: "Thierry had encouraged his team-mates to go and acknowledge the fans and show their appreciation for the people who made the long journey to Swansea.
"Unfortunately, one or two of them had a few things to say and expressed their disappointment.
"One in particular was shouting: 'Where is the heart and the character and the fight?' Thierry shouted back: 'Get behind the team and support the players and don't be negative.'"
Having come on to score the winner against Leeds in the FA Cup last week, Henry could not repeat his heroics, and Gunners boss Arsene Wenger admitted he had been tempted to give him a starting berth.
"You are always tempted to start him," said Wenger. "When he comes on the pitch he gives us a lift. He was dangerous again."