The Blades came from 1-0 down at half-time to build up a 2-1 lead at Oakwell via John Fleck and Leon Clarke goals in the second period.
They then looked on top in a thrilling South Yorkshire derby - only to concede a scrappy equaliser and subsequently see Tom Bradshaw head home an 88th minute winner for Barnsley.
United had drawn their previous three games and have now won just once in their last seven outings as they missed a glorious chance to - temporarily at least - edge into the Championship top-six.
Wilder said: “I've got to say, of the two teams - one wanting to stay in the division and the other wanting to get out of the division - I thought the team who wanted to stay in the division were better in the first half.
"They won more first and second balls, played quicker, played with more intensity. We looked a little bit leggy, we played far too slow, backward and square in the first half and when we did get into our stride a couple of times in the first half I thought we looked dangerous.
"Knowing what my team's about, we got into them a bit at half-time, made a couple of changes and then got into our stride, got into our rhythm, built pressure and built momentum.
“From then we took the game away from the opposition and I've got to say from 2-1, we should go to 3-1 and 4-1.
"But yet again, boring everybody that interviews me after every game, it's the clinical bit (we’re missing) that kills teams off by going three and four one. It demoralises them.
“Or the other side of it, when a side sticks the ball in the box, you defend it properly.
“The second and third goals from my point of view are really poor ones.”
His side have now slipped to ninth, four points behind sixth-placed Middlesbrough who they host on Tuesday.
Wilder continued: “At 2-1 it looked as if the opposition had gone but - and I’m sick of saying it we just don’t have the ability…. (to finish teams off).
“We play some great football at times and look a really good side.
“But really good sides have got to win the other Friday (at Brentford). You can’t create all those chances and not win. You can’t play as well as we did on Monday night (versus Cardiff) and then yet again see one hopeful ball into our box punish us.
“That really is, from my point of view, the frustrating thing about it all.”
Barnsley boss Jose Morais was delighted as his side secured their first home victory under his management and a first at Oakwell in 13 games.
The Tykes went ahead through Gary Gardner before Fleck and Clarke struck but they reallied superbly as Oli McBurnie and Bradshaw got them the win that leaves them just two points adrift of safety with a game in hand.
A beaming Morais said: "I wanted to give the smile to the people since long ago and I was holding the smile the whole time.
“I'm happy to be here today, that we won and this is the smile I have every day.
"I wanted to say that we were trying to find reasons we couldn't do it before, and this was the work we have been doing since we've arrived here.
"The work was to try to find the belief in themselves and the belief from themselves in the team quality, the team capacity, besides the belief they have in their own qualities. It has been improving.
"This is what they showed today, that everything is possible when we really are committed to achieve and we trust each other to be able to turn around difficulties into something positive.
"I want to see it as a turning point, because it is."