The Blades are without a win in five Championship games after slipping to another defeat at Bristol City on Saturday evening.
United are winless on the road since December and have taken just one point in the away fixtures against the three sides promoted from League One last season.
Goals either side of the break - from David Noble and Michael McIndoe - sealed Bristol City's victory.
For the trip to Ashton Gate, Robson made two changes, one enforced due to the injury sustained by Gillespie in midweek. Bromby dropped to the substitutes bench with Carney, making his full Championship debut, and Lucketti brought in to the starting line-up.
United, looking to end the away hoodoo, made a bright start and could have been ahead after just 30 seconds. From Armstrong's cross, Beattie got ahead of his marker and forced Basso into a save, at the second attempt.
Stead also had a pot-shot which was wide before the home side found a rhythm and forced the Blades onto the back foot.
McIndoe fired a free-kick into the wall and then Byfield found himself free on the left but his shot was comfortable for Kenny. Morgan conceded a second free-kick on 11 minutes but from a well-worked routine, Fontaine could only direct wide under pressure from the recalled Lucketti.
The City fans thought they had taken the lead on 15 minutes when, from a corner, Orr headed against the crossbar. It wasn't clear from the naked eye but the replays showed that Kenny had added a vital touch to tip the ball onto the crossbar.
McIndoe also fired over before United began to get a foothold in the game. Stead shot over after being heavily involved in the build up on 20 minutes and then Carney's effort was straight at Basso.
From Hendrie's volleyed cross, Cahill could only direct the ball wide with his shoulder before the home side went back on the offensive . Despite conceding a number of set-pieces, United did well to stifle the home side, who could only manage a long-range effort from Elliott, which was straight at Kenny.
However, just before the break, Bristol City's pressure paid off. From a ball through the middle, Morgan's attempted header back to Kenny was short and NOBLE nipped in, flicked the ball over the goalkeeper and managed to steer it home, despite the presence of Armstrong.
Despite the goal coming on the stroke of the interval, United still had time to mount another attack and following a free-kick and corner, Quinn powered through the defence and fired against a post before City scrambled away the rebound, just prior to referee Taylor's half-time whistle.
Stephen Quinn was introduced at the break but it was his elder brother who was in the thick of the action early in the second half, picking up a booking for an off-the-ball clash with Carey.
The side's exchanged chances before the hour when Carney's effort on the turn was over and then McIndoe forced a save from Kenny, diving to his right.
Robson used the second of his replacements when Shelton replaced Stead but Carney forced the first real save from Basso, when the goalkeeper turned over after the Australian had cut in from the left. From the resulting Alan Quinn corner, Lucketti won the header but McAllister directed the ball wide of the post.
City weathered the storm and went back on to the attack and on 63 minutes went close to adding a second. Sproule found himself clear on the right but Kenny made a fine save and the rebound hit Tonge as United survived another scare.
However, that wasn't the case on 71 minutes when the home side added a second. Sproule powered down the right and his cross from the line was met by McINDOE, who appeared between the defence and gave Kenny no chance from inside the six-yard area.
United needed to throw caution to the wind but were still unable to trouble the City defence. The home side introduced Trundle and Lucketti was booked for a foul on the former Swansea striker.
Carey powerfully shot wide and the introduction of Sharp proved to be too late to make a difference as United failed on the road yet again. Three minutes of injury-time were added but the visitors were unable to replicate the heroics of Tuesday evening and slipped to 20th place in the Championship.
Bristol City: Basso, Orr (McCombe 67), McAllister, Fontaine, Carey, Noble (Skuse 74), McIndoe, Elliott, Sproule, Johnson, Byfield (Trundle 79).
Unused: Murray, Henderson.
Blades: Kenny, Morgan, Beattie, Stead (Shelton 60), Hendrie (S. Quinn 45), A. Quinn, Carney, Tonge, Armstrong, Cahill, Lucketti (Sharp 88).
Unused: Bromby, Kilgallon.
