Lukas Podolski and Olivier Giroud found the net in the space of one second-half minute to turn the game on its head after Wilfried Bony had given Swansea an early lead, but Mathieu Flamini scored an own goal to pull the visitors level at the death.
However, referee Lee Probert then decided to blow for full-time with Swansea's Jonathan de Guzman clean through on goal just inside the Arsenal half, drawing the ire of head coach Monk.
"Very poor decision," he said. "First half, they added two minutes on because of our goal - fair enough.
"So they told us it was going to be four minutes at the end of the game - OK.
"We score in that period, so they add an extra minute on, so that's five minutes minimum - I'll stress the word 'minimum'.
"And then we're clean through on goal, 99 per cent a goalscoring opportunity is going to come and they blow up 30 seconds short.
"A very poor decision, as simple as that.
"I'm not going to say whether he's going to score the goal or not - I can't predict that - but it's definitely going to be a shot on goal."
Probert was surrounded by Swansea players at the final whistle, but Monk conceded he was happy to register an important point, which lifts them five clear of the relegation zone.
"If you offered us a point before the game we would have said yes," he added. "Every point is vital.
"I had more belief in this team than a lot of other people and I know what they can do and they showed that tonight.
"My final word before they went out was to be together and do it for each other, because at the end of the day when you're out there that's all you've got and they did it to a man."
