Arsenal could not contain their anger after succumbing to a defeat that leaves them struggling to hold on to Chelsea's coat-tails in the race for the Champions League qualification places. First Thierry Henry became involved in a row with one of the travelling supporters. Then Arsène Wenger fiercely criticised Michael Oliver, the referee, accused Nathan Dyer of diving to win a penalty and lambasted a dreadful defensive performance from his team.

Henry's set-to with an Arsenal fan came after the final whistle, when the players went across to applaud their followers. It is understood the striker, who had replaced Andrey Arshavin in the 63rd minute, clashed with the supporter after taking unkindly to his criticism of the players, the Frenchman telling him that he should support rather than berate the side.

According to a club spokesperson Henry had said: "No matter what, you should support the team." The 34-year-old, making the second appearance of his loan from New York Red Bulls, also appeared to make a 'yapping' gesture at the fan with his left hand and pointed as if to invite the individual to address him on the pitch.

These incidents should not take all the attention from Swansea. Wenger, amid his rant, gave credit to the Welsh side, acknowledging they deserved to win a compelling game that will live long in the memory in these parts. Danny Graham delivered the final blow, the Swansea striker shooting across Wojciech Szczesny 45 seconds after Theo Walcott had hauled Arsenal back to 2-2. Arsenal could still have salvaged a point but a gilt-edged chance dropped to Per Mertesacker and the Germany international inexplicably sliced wide from inside the six-yard box, leaving Wenger struggling to come to terms with the outcome.

"Swansea played well but the game was decided by some strange decisions – the first one was the referee who gave a penalty that was a complete imagination and was a good dive. Well done to the player who did it," Wenger said. "And from then on I feel there were some other turning points, like when we came back to 2-2 we made straight away a defensive mistake, similar to Fulham [a late 2–1 defeat after leading 1–0], where there was a lack of appreciation of the goal.

"Our defensive performance was not good enough and that's why we lost the game. When we came back to 2-2, I thought we had a good chance to win the game. Their keeper made some great saves and we also missed some unbelievable chances that are very difficult to understand and explain. But apart from all that, well done to Swansea, they played well and they deserved to win."

With that Wenger got up and departed after answering one question, the Frenchman providing a couple of terse responses to inquiries about Arsenal's defensive problems as he headed out of the conference room. He had spent the best part of 10 minutes waiting for Brendan Rodgers to finish his media duties and a police escort was waiting to take the Arsenal bus back to the airport, although this sobering result gave him another good reason to get out of the Liberty Stadium as quickly as possible.

The penalty award that upset Wenger looked soft but Aaron Ramsey appeared to make slight contact with Dyer's ankle, prompting Oliver to point to the spot and give Scott Sinclair the chance to bring Swansea level after Robin van Persie had earlier beaten Michel Vorm at his near post. In that context Wenger's criticism of Dyer, who was the game's outstanding performer on an afternoon when Fabio Capello had come to watch another English winger (Walcott), seemed harsh.

There was certainly no argument with Wenger's assessment of Arsenal's defensive display, especially for the second and third goals. Arshavin, who set up Van Persie's opening goal but was otherwise anonymous and predictably withdrawn in the second half, played a careless pass to Ramsey that allowed Joe Allen to pinch possession in the lead-up to the second goal. On the third Laurent Koscielny was caught out of position, with Arsenal failing to take heed of the adage that a team are most at risk of conceding straight after scoring.

That is enough criticism of Arsenal. This was a hugely impressive Swansea display that demonstrated they have resilience within their ranks as well as flair. Ashley Williams was outstanding at the back, Allen provided some lovely touches in central midfield and Dyer carried a threat whenever he got the ball, his penetrative runs making life difficult for Ignasi Miquel, the Spanish defender who was making his first Premier League start, and just about everyone else in the Arsenal defence who tried to stop him.

There were raucous scenes at the final whistle as Rodgers punched the air after a win that lifts Swansea to 10th place. "It was a wonderful victory and performance from us. I'm very proud of the players and it's a great day for the people and the city of Swansea," said the manager, who made a point of highlighting how well his English front three – Dyer, Graham and Sinclair – played in front of Capello. "They were a massive threat and it's probably given him something to think about."