However, he should also try to destroy any evidence of the first 45 minutes which were as bad as anything else at Bramall Lane this season.
Defeat, ultimately, was cruel on the Blades who trailed 2-0 at the interval due to a brace of goals from Jay Simpson but got back on level terms courtesy of two goals from Ched Evans.
As the final whistle loomed, the Blades had looked the more likely winners but then, deep into stoppage time, Hull substitute Jimmy Bullard settled the contest after a great solo run by winger Cameron Stewart. Bullard scored from close range after Blades goalkeeper Steve Simonsen only half saved Stewart's low drive.
Carver had stuck with the same 11 players who secured victory over Swansea City in his first game at the helm since the departure of Gary Speed.
Hull were without suspended left-back Andy Dawson so manager Nigel Pearson recalled Kevin Kilbane in the only change from the win over Bristol City. Bullard was on the bench after two months on the sidelines with a knee problem.
The Tigers got off to the perfect start, taking the lead after just three minutes.
Stewart sped away from defender Nyron Nosworthy and his pull back found Simpson who tucked the ball home from eight yards.
Simpson had gone 15 games without a goal following his summer move from Arsenal but now boasted three in two after scoring both in the win over Bristol City.
The Blades soon suffered another setback with defender Andy Taylor leaving the field on a stretcher.
Taylor, who was hurt in a challenge with Ian Ashbee on the edge of the Hull area, was replaced by youngster Matthew Lowton.
Hull would also lose their leftback Kilbane to injury as the game began to hot up.
Kilbane suffered a nasty gash to the head and was replaced by Paul McShane.
Tension started to surface and not just on the field of play.
Stewards arrested a Hull supporter who had come over the advertising hoardings and others in the away end appeared intent on sparking disharmony.
When Hull's Anthony Gerrard caught Quinn with a late challenge it led to the game's first melee. Gerrard was booked along with Blades winger Andy Reid for leading the protests.
The distraction from play was not completely unhelpful at this stage as some of the football was low on quality.
Blades supporters sat in silence for long periods of the first half – adopting the attitude of saying nothing when having nothing good to say.
The Blades may have been trying to knock the ball around but committed far too many unforced errors in possession.
As a player on loan from Arsenal, young defender Kyle Bartley should have been an exception to the rule. However, even he was off his game and became the butt of mocking chants from the away end.
At various stages, Montgomery, Reid, and Lowton were all guilty of over-hitting long balls in the first half.
When Evans hoofed a 50-yard pass to the Hull goalkeeper, it sparked cries of incredulity. There were ironic cheers when Quinn had to limp off just before the break but things were about to get even worse for the Blades.
Simpson exposed Nosworthy's lack of pace for the second time in the game and was tripped by the defender inside his own area. Referee Scott Mathieson duly awarded a penalty and Simpson doubled Hull's lead from the spot.
The patience of the home supporters snapped and, inevitably, there was widespread booing at the half-time whistle.
From Hull's perspective, things could hardly have been going better. Mind you, Bullard was sent tumbling to the floor during a kick-about with schoolchildren at the break and, with his injury record, that could have been a nightmare going into the New Year transfer window.
The Blades showed signs of intent at the start of the second half with Carver switching to a 4-4-2 and playing substitute Jamie Ward in attack with Evans.
But Hull also showed why they have one of the best defensive records in the Championship (only leaders Queens Park Rangers have kept more clean sheets) and the Blades had to wait until the 63rd minute to get back in the game. Evans provided the lifeline, rising to head Reid's cross beyond the reach of goalkeeper Vito Mannone.
Tempers flared again when Ashbee reacted angrily to a tackle by Montgomery in the centre of the pitch. The Hull captain kicked out and sparked a melee involving 20 players.
Blades defender Bartley was held back by Hull's goalkeeper Mannone, a team-mate in Arsenal's reserves, but was still fortunate to stay on the field after appearing to throw a punch and aim a kick at a Hull player.
As the game entered its last quarter, the Blades were in the ascendancy with Hull desperately trying to cling on to their lead.
Evans levelled with a goal that needed real determination and a cool head. The Welsh striker beat the Hull offside trap and then slid in as goalkeeper Mannone attempted to gather.
Mathiseon ruled no foul and Evans duly found a gap between defenders on the line to find the net from a tight angle.
Hull might have been awarded a penalty when Stewart was sent tumbling to the floor by Calve but it proved irrelevant when Bullard snatched the winning goal deep into stoppage time.