'Quite unbelievable' as Garry Monk reflects on Sheffield Wednesday draw
The Owls hit the post three time, had a Steven Fletcher 'goal' disallowed, and spurned chance after chance to score.
But all they had to show for their efforts were goals from Fernando Forestieri and Morgan Fox - after Andre Ayew had put the visitors in front - meaning Ben Wilmot's stoppage-time header saw Wednesday drop two valuable points.
Monk said: "It was very frustrating in the end.
"The effort and commitment is there and it's clear they're fighting hard for each other, but set-pieces in the last two games have cost us.
"You need to focus on what you've trained very hard to do. The roles are very clear and you need to focus on what you need to do but unfortunately we haven't done that in those two critical moments in the last two games.
"We probably should be stood here with six points from the last two games but we have the one.
"How the ball didn't go in for us in the first half is quite unbelievable. To fight back and get that lead shows there's a lot of effort and commitment.
"There's a lot of positives but of course there's work to be done during the international break ahead of our busiest period when we come out of it."
Wednesday will wonder how they failed to score more than their two goals.
Jacob Murphy saw his early effort saved by Freddie Woodman, who pushed the ball onto his left-hand post.
Fletcher then headed against Woodman's left-hand post.
Swansea took the lead against the run of play when keeper Keiren Westwood failed to deal with a Matt Grimes corner and Ayew pounced on the loose ball.
Wednesday hit the woodwork for a third time just after the hour mark when Murphy smashed the loose ball against Woodman's left-hand post after Fletcher's header was saved.
Ayew put his header wide and Wilmot then headed against a post.
Wednesday equalised when Adam Reach's low drive was parried by Woodman and the ball eventually fell for Forestieri to finish from close range.
Fox struck in added time after Dominic Iorfa headed down following a corner before Wilmot equalised with a far-post header from a Grimes corner.
Swansea are now unbeaten in 10 league games away from home and Swans boss Steve Cooper admitted he was happy to leave Yorkshire with a point.
Cooper said: "I guess there's a little bit of relief, having gone 2-1 down and thinking the last thing we deserved was not to get a win today.
"It's a difficult place to come and I thought Sheffield Wednesday started the better. They're a real threat with the way that they play, but we managed the storm and then just completely controlled the game in the first half.
"You just want to see the game out but we conceded a couple of soft goals from our point of view.
"I'm just pleased that we didn't lose because it would have been a travesty after the way we played.
"In the end, we're quite pleased that we got a point but we created some really good chances. We're having to work hard for every point."