Chris Wilder felt Sheffield United showed a lack of leadership to concede the goal which consigned them to another season in the Championship.
Anel Ahemedhodzic was off the field injured when Tommy Watson put Sunderland in front for the first time in the play-off final five minutes into stoppage time.
To go 2-1 up at that stage left the Blades with no time to respond.
But Wilder felt they should have coped better with being a man light, Kieffer Moore giving the ball away Watson, who was able to carry the ball to within shooting distance and produce a shot which left Michael Cooper with no chance.
It was only Sunderland's third shot on target after Sheffield United had dominated the first half and kept their opponents at arms length for much of the second.
"You've got to put teams to bed and you've got to be clinical and you've got to be tidy and you've got to be smarter," said Wilder.
"We weren't smart in terms of our organisation on the second goal, you're into the 97th minute of a game and we're sort of strung across the middle of the park.
"The boy (Watson) finds an enormous amount of space to counter and break on us.
CRITICISM: Sheffield United manager Chris Wilder (Image David Klein / Sportimage)CRITICISM: Sheffield United manager Chris Wilder (Image David Klein / Sportimage)
CRITICISM: Sheffield United manager Chris Wilder (Image David Klein / Sportimage)
"Sit in as a 4-4-1 or sitting as a 4-5(-0), really, and see that final 30 seconds out or a minute because Anel was potentially coming back on.
"We didn't really want to make a decision on Anel because of the importance of substitutes in extra-time. had that ability to bring one on.
We would have had the ability to bring another one on and I think that would have been a crucial point, but to lose it.
"To lose it in that manner really stings.
HEARTBREAK: Tom Davies (right) consoles Andre Brooks (Image: David Klein / Sportimage)HEARTBREAK: Tom Davies (right) consoles Andre Brooks (Image: David Klein / Sportimage)
HEARTBREAK: Tom Davies (right) consoles Andre Brooks (Image: David Klein / Sportimage)
"Whether it's lack of experience or a bit of leadership where we just go we just see the game out but that wasn't to be and they find a fabulous winner."
Tyrese Campbell put them in front through a well-worked goal created by Gustavo Hamer, who later went off injured.
But they had a Harrison Burrows goal disallowed on review in the first game either side has played this season with a video assistant referee, Vinicius Souza deemed to be interfering with goalkeeper Anthony Patterson's attempt to save the shot.
Then Andre Brooks missed a great chance to put his side 2-0 up shortly before Eliezer Mayenda equalised.
"There were certain times in the game we can look at from our point of view, where we needed to be better with and the opportunities that have come around for the opposition, they've taken and punished us severely," he said.
"We started off really well and on the front foot. We found our moment with Ty.
"There'll obviously be a lot of talk about the VAR. We play 46 games and two play-off games (without VAR), and then all of a sudden it's a subjective decision by the referee
"I don't think the goalkeeper saves it. I don’t think he gets anywhere near it. I think it’s gone past him. But listen, that's by the by.
"Our goalkeeper’s not really had a save to make.
"We started getting back in control of the game 10 minutes into the second half, and we had a couple of chances. When a team has to open up and go for it, which they did, and we'd have been the same. We were too loose in transition and on the counter-attack.
"We gave up some really good, clean opportunities to go and punish them. And if we got the second, then I think we win the game.
"On the sideline I never felt worried and that we needed to do something. But the two goals from our point of view are really poor.
"They found the finishes, but for the second goal we need to secure the ball at the top of the pitch but we don’t and the middle of the park is wide open.
"And then the game's gone past us, it's 97 or 98 minutes. So fairytale stuff for the boy and for Sunderland. For us, it's going to take quite a while to get over."