Lyle Taylor's first goals in a Blades shirt almost inspired a magnificent recovery.
The summer signing netted twice in the second half but the Blades were already 3-0 down at Coventry City's exiled Sixfields Stadium home.
Following the departure of David Weir 48 hours earlier, Chris Morgan, assisted by goalkeeper coach Darren Ward and Academy coach Travis Binnion, was in interim charge of the Blades, who remain without a win on the road this season.
Long and King were given the green light to play for United, despite being called up for international duty, and were both selected by interim boss Morgan, who also brought back Flynn. Maguire shook off a knee problem to play, but McMahon's thigh problem kept him out.
It quickly became evident that the wet pitch would be a factor and United were forced to concede an early corner before Coventry grabbed the lead on six minutes. A deep, deflected Adams cross found Leon CLARKE in space and he directed the ball beyond Long's left hand.
The Blades attempted to hit straight back and King headed Hill's cross wide but Coventry had made the better start. Thomas had an effort deflected wide and Clarke headed wide from another deep cross.
Just after the half hour the Blades fell further behind. This time Baker found room on the right and his low cross saw WILSON get away from Coady to direct the ball into the top corner. It could have been worse moments later but Clarke, despite getting free, shot at Long.
Baxter curled a free-kick over the crossbar as the Blades pushed Coventry back late in the half but again a crucial decision went against the club. Coventry's Webster had only been booked a moment earlier for a foul on Baxter and when he did likewise to Brandy many inside Sixfields thought a red card was on the way but referee Dean opted to just speak to the defender.
Taylor replaced Baxter, who was struggling with a thigh problem and before the break the referee was again in thick of the action when he showed a yellow card to Maguire when the Blade was adjudged to have fouled Wilson, who was bounding through on goal.
A goal was needed early in the second half and, unfortunately, it was scored by Coventry. A run from Brandy gave Blades fans hope but within seconds Wilson had flicked on, Moussa held off Westlake and Leon CLARKE was given the space to curl into the bottom corner to make it three.
Coady's run set up an opportunity for Brandy on 56 minutes but his effort was saved by the legs of goalkeeper Murphy and moments later King was replaced by McGinn, whose first action was to whip in three successive corners.
The momentum was now with the Blades and there was a glimmer of hope on 62 minutes following a foul on Coady by Willis. From the free-kick, 20 yards out, TAYLOR's blast penetrated the Coventry wall and beat the goalkeeper. It could have been two a minute later when Webster's back header gave Flynn a chance but his shot was saved by Murphy.
Two Coady headers kept United on the front foot. He headed over a McGinn corner and then he threw himself at a Westlake cross but the diving header was just over. Morgan used his last replacement, Hall taking over from Flynn, whilst Clarke was denied a hat-trick by Long's smart save.
United got within one on 80 minutes to give the 966 Blades fans inside Sixfields more hope. Coady laid off to Hall and his cross found fellow substitute TAYLOR, who headed into the bottom corner.
Coventry responded by making their third change and soon after 'home' goalkeeper Murphy needed lengthy treatment after a collision with one of his own defenders.
Late on - and six minutes of added time - saw the Blades primarily on the attack and committing bodies forward. From a Hall cross, McGinn's deflected header was saved by the fully-recovered Murphy, whilst at the other end Maguire's header off the line prevented Clarke adding his own third and Fleck curled over.
Time, though, ran out and despite the brave fightback the final whistle signalled that the Blades had slipped back to the bottom of League One.
Coventry: Murphy, Adams, Webster, Thomas, Fleck, Baker (Daniels 67), L. Clarke, Moussa (Barton 81), Willis (Phillips 77), Wilson, J. Clarke.
Unused: Manset, Burge, Garner, Haynes.
Blades: Long, Westlake, Maguire, Hill, Flynn (Hall 73), Doyle, Baxter (Taylor 41), Collins, Coady, King (McGinn 57), Brandy.
Unused: Howard, Lappin, Murphy, Ironside.