The Gunners took the lead just past the half-hour mark courtesy of Nacho Monreal but fell apart as Swansea scored three.
Sam Clucas scored the equalizer within 2 minutes before Jordan Ayew gave them the lead in the second-half and Clucas added a third, four minutes from time.
With the result the Gunners’ hopes of making the top four has been dented as they are now eight points adrift of Liverpool who won comfortably 3-0 at Huddersfield.
Arsene Wenger questioned his players’ discipline and blasted them for making “big mistakes”.
He told BBC Sport, “I felt defensively we were very poor and made big mistakes.
“It’s better not to talk about the second or third goals.
“Swansea were sharp, disciplined and hungry. Unfortunately I believe we were not good enough, I believe we were not disciplined enough.
“I don’t want to talk about second or third goals.”
The match was also likely to be Olivier Giroud’s last for the club as he edges closer to a move to Chelsea.
And Wenger admitted after the match the France international’s future would be resolved tomorrow on deadline day.
When asked if Giroud had played his final game for the Gunners, he replied: “It’s a possibility.
“But all that will be decided tomorrow morning. We will inform you once that is more definite.”