After a slow start to proceedings in testing, wet conditions in Wales, Alexis Sanchez opened the scoring in the 63rd minute after a flowing Arsenal move.
Gylfi Sigurdsson equalised with a free-kick in the 75th minute before replacement Bafetimbi Gomis scored what proved to be the winner three minutes later when he rose highest to steer home a Jefferson Montero cross.
It was the second highly disappointing result inside a week for the Gunners, after they let a three-goal lead slip in midweek to draw 3-3 with Anderlecht in the Champions League.
Wenger dismissed much of the criticism that was directed at his side after their European stutter, but he was in a less forgiving mood after Sunday’s loss
“It’s disappointing to throw a game away like we did. We were 1-0 up and had to be tight defensively and wait for that second chance. But you have to credit Swansea who didn’t give up,” lamented the Frenchman.
“In football you can believe anything is possible, any minute you can concede. Bafetimbi Gomis is good in the air and it can happen. You have to accept that Swansea will fight until the last minute. We eased off at 1-0 and let them back into the game.
“Football is down to performances. We are here to produce performances, and didn’t do that right until the end of the game.”
The result sees Swansea climb above Arsenal in the league standings and into fifth position.