Chris Wilder says his Sheffield United players "chucked it away" and must improve their mentality if they are to climb out of trouble after losing to Luton in an extraordinary game.
The Blades fought back from 1-0 behind to lead 2-1 only for the Hatters to secure victory after two own goals in the space of four minutes.
A 14th Premier League defeat leaves Wilder's side stuck at the bottom of the table seven points from safety before a trip to Manchester City on Saturday.
"We really should be talking about a home win. We really should be talking about us getting a third win [in the league], not throwing it away," added Wilder.
"There has been a lot of positivity lately but this is a backwards step that hurts."
Asked if his players were feeling sorry for themselves, Wilder said: "I don't give a monkey's how they feel. They are professional footballers.
"Everyone has to be accountable. These boys have got to have that attitude of being strong mentally."
A howler by Wes Foderingham gifted Luton the lead when Alfie Doughty's 17th-minute attempt slipped through the keeper's legs into the net.
The Blades thought they had turned it around after the interval, Oli McBurnie equalising after Sam Allison - the first black referee to take charge of an English top-flight match for 15 years - played a smart advantage when James McAtee appeared to have been fouled.
With fellow strugglers Nottingham Forest winning earlier at Newcastle, the Blades needed all three points and captain Anel Ahmedhodzic fired them in front from close range after Luton failed to clear.
But two own goals - first a flicked header by Jack Robinson and then by substitute Anis Ben Slimane - allowed Luton to seal back-to-back Premier League wins after their 1-0 victory over Newcastle last Saturday.
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Blades throw it away
Sheffield United will wonder how they let this lead slip after producing a stirring fightback in the second half.
After a recent improvement in results since Wilder returned earlier this month, this was a worrying step in the wrong direction.
After conceded an equaliser deep into stoppage time in the previous game at Aston Villa, they again failed to hang onto the lead against Luton.
They have reached the halfway stage of the season with just nine points on the board.
Wilder now has the job of lifting his players after a highly damaging defeat.
"We handed them the game," added the Blades boss. "We can only look at ourselves. We have to get back on the bike pretty quickly. You can't just turn a game over like that."
Hatters show incredible spirit
Luton's players celebrated in front of their own fans after a significant win that strengthens their hopes of climbing out of trouble.
The Hatters remain in the bottom three but are just one point from safety, with out-of-sorts Chelsea the visitors to Kenilworth Road on Saturday (12:30 GMT) as they hunt a third successive league win.
After the trauma of captain Tom Lockyer having cardiac arrest on the pitch at Bournemouth, Luton have shown incredible spirit to secure six points from their past two games which could be crucial to securing their Premier League future.
"I don't know," said boss Rob Edwards when asked if what happened to Lockyer had brought his squad even closer together.
"I get we have won two games in a row but we have been playing well for some time now.
"That said we do want to embody what Tom is. He has been such a success in football because of his bravery."
Luton looked down and out after falling 2-1 behind but somehow emerged with a win from a remarkable encounter.
Carlton Morris came off the bench and orchestrated the turnaround, with first Robinson and then Ben Slimane putting through their own net to leave the Blades bereft.
Player of the match
BarkleyRoss Barkley
with an average of 7.98
Sheffield United
Squad number10Player nameArcher
Squad number28Player nameMcAtee
Squad number9Player nameMcBurnie
Squad number8Player nameHamer
Squad number2Player nameBaldock
Squad number15Player nameAhmedhodzic
Squad number21Player nameVinicius Souza
Squad number35Player nameBrooks
Squad number19Player nameRobinson
Squad number5Player nameTrusty
Squad number3Player nameLowe
Squad number32Player nameOsula
Squad number7Player nameBrewster
Squad number18Player nameFoderingham
Squad number25Player nameBen Slimane
Squad number16Player nameNorwood
Luton Town
Squad number6Player nameBarkley
Squad number45Player nameDoughty
Squad number5Player nameAndersen
Squad number28Player nameSambi Lokonga
Squad number30Player nameTownsend
Squad number7Player nameOgbene
Squad number9Player nameMorris
Squad number19Player nameBrown
Squad number29Player nameBell
Squad number2Player nameOsho
Squad number15Player nameMengi
Squad number24Player nameKaminski
Squad number11Player nameAdebayo
Squad number17Player nameMpanzu
Squad number26Player nameGiles
Line-ups
Sheff Utd
Formation 4-4-2
- 18Foderingham
- 2BaldockBooked at 78mins
- 15AhmedhodzicBooked at 14mins
- 19RobinsonBooked at 79minsSubstituted forBrewsterat 86'minutes
- 5Trusty
- 28McAtee
- 21de Souza CostaSubstituted forNorwoodat 86'minutesBooked at 90mins
- 35BrooksSubstituted forLoweat 45'minutes
- 8HamerBooked at 41minsSubstituted forBen Slimaneat 72'minutes
- 9McBurnie
- 10ArcherSubstituted forOsulaat 86'minutes
Substitutes
- 1Davies
- 3Lowe
- 7Brewster
- 16Norwood
- 23Osborn
- 25Ben Slimane
- 32Osula
- 33Norrington-Davies
- 38Seriki
Luton
Formation 3-4-2-1
- 24Kaminski
- 15Mengi
- 2Osho
- 29Bell
- 45DoughtySubstituted forAndersenat 78'minutes
- 28Sambi Lokonga
- 6Barkley
- 26GilesSubstituted forOgbeneat 72'minutes
- 30TownsendSubstituted forMpanzuat 84'minutes
- 19Brown
- 11AdebayoSubstituted forMorrisat 71'minutes
Substitutes
- 1Shea
- 5Andersen
- 7Ogbene
- 8Berry
- 9Morris
- 10Woodrow
- 14Chong
- 17Mpanzu
- 23Krul
Referee:Sam Allison
Attendance:31,041
Live Text
Match ends, Sheffield United 2, Luton Town 3.
Second Half ends, Sheffield United 2, Luton Town 3.
Attempt missed. Auston Trusty (Sheffield United) left footed shot from the centre of the box is high and wide to the left following a set piece situation.
William Osula (Sheffield United) wins a free kick on the right wing.
Foul by Amari'i Bell (Luton Town).
Foul by Oliver Norwood (Sheffield United).
Pelly Ruddock Mpanzu (Luton Town) wins a free kick in the attacking half.
George Baldock (Sheffield United) wins a free kick in the defensive half.
Foul by Carlton Morris (Luton Town).
Foul by Auston Trusty (Sheffield United).
Jacob Brown (Luton Town) wins a free kick in the defensive half.
Attempt missed. Anel Ahmedhodzic (Sheffield United) right footed shot from outside the box misses to the left.
Oliver Norwood (Sheffield United) is shown the yellow card for a bad foul.
Foul by Oliver Norwood (Sheffield United).
Pelly Ruddock Mpanzu (Luton Town) wins a free kick in the defensive half.
Corner, Sheffield United. Conceded by Teden Mengi.
Attempt missed. Anis Ben Slimane (Sheffield United) right footed shot from the right side of the box is too high. Assisted by George Baldock following a set piece situation.
Foul by Teden Mengi (Luton Town).
Oliver McBurnie (Sheffield United) wins a free kick on the left wing.
Foul by Jacob Brown (Luton Town).