Lifelong supporter Adams had seen little of the Blades this season due to the demands of his previous job as manager of League Two Port Vale.
But after this torrid afternoon at Turf Moor, Adams will be under no illusions about the size of his task.
"As a manager, you get used to defeats but this is the first time I've been manager of a team I follow so defeat hurts twice as much," he said.
"I don't think we rolled over and let Burnley tickle our bellies but it can only get better. The way we defended was not the best – and that's being very nice!"
With less than 48 hours to prepare for today's game against Doncaster Rovers, Adams will find it difficult to implement immediate change.
"I would like to think that I can improve the defending but I need time on the training ground," he said. "There were players on the bench today and I didn't even know their names!
"We can't feel too sorry for ourselves because the games are coming thick and fast," he stressed. "There are some decent characters in that dressing room and I think they are hurting. I will have to put a plaster on a few egos."
Adams had walked into the Blades job missing four players due to suspension and five due to long-term injuries.
Nick Montgomery, Kyle Bartley, Stephen Quinn and Andy Reid were banned while Andy Taylor recently joined Darius Henderson, Chris Morgan, Stephen Jordan and Ryan France on the treatment table.
Taylor, stretchered off against Hull City on Boxing Day, is out for the rest of the season after snapping cruciate knee ligaments.
Midfielder Lee Williamson started his first game since recovering from back surgery in the summer. Leon Britton returned after missing the trip to Norwich City and there were recalls for Matthew Lowton, Johnny Ertl, and goalkeeper Richard Wright.
However, Adams had to fill the bench with a trio of youngsters – Jordan Slew, Kingsley Black and Matty Harriott.
Burnley caretaker-manager Stuart Gray made four changes for his first game in charge since the sacking of Brian Laws.
Andre Bikey, John Guidetti, Ross Wallace and Jack Cork dropped to the bench with Michael Duff, Dean Marney, Chris Iwelumo and Chris Eagles winning recalls.
The Blades lined up in a 4-4-2 formation with stand-in captain Richard Cresswell wide on the left and Jamie Ward alongside Ched Evans in attack. Ertl deputised for Bartley at centre-back and Williamson and Britton formed the central midfield pair.
After a nervous opening few minutes, the Blades settled down and silenced the Turf Moor crowd with an early goal.
Mark Yeates scored from 10 yards out after Burnley goalkeeper Lee Grant was unable to hold a vicious low drive from Ward.
It was a dream start for Adams and assistant Alan Cork, who had already been serenaded by the Blades away support. However, Burnley got back on level terms just before the half hour when Chris Eagles beat goalkeeper Wright from 25 yards.
Former England international Wright was making only his second start for the club and had produced two important saves to deny Iwelumo and Rodriguez.
Wright may feel he could have done more to prevent the equaliser although it was Nyron Nosworthy's loose clearance that gave Eagles the ball.
Things got even worse for Nosworthy when he was caught napping for Burnley's second on the stroke of half-time.
Nosworthy switched off on the edge of the area and allowed Iwelumo to score with a free header.
Just over a minute later, Rodriguez made it 3-1 to the home side, arriving at the far side of the box to drill home Elliott's cross.
From a healthy position 1-0 up, 15 minutes before half-time, the Blades had messed up and Adams was faced with giving a completely different pep talk than should have been the case.
Wright and Nosworthy had suffered injuries so Adams sent on Steve Simonsen and Elian Parrino, the young Argentine defender who had not been on the field since signing from Estudiantes two months ago.
Parrino held his own against the aerial threat of Iwelumo and drew praise from his manager after the game.
The Blades were handed a lifeline less than a minute after the re-start when referee Robert Shoebridge ruled that Duff had tripped Evans in the box. Evans slammed in the penalty and suddenly it was game on again.
The Blades weathered spells of heavy pressure and Simonsen was only rarely put to the test in goal.
With Williamson tiring, Adams sent on striker Daniel Bogdanovic and moved Cresswell into the centre of midfield.
Ward found Bogdanovic at the far post from a free-kick but the striker's shot was straight at goalkeeper Grant.
With five minutes to go, substitute Steven Thompson settled the contest. The striker collected a pass from Eagles, squeezed between Calve and Ertl, and poked the ball beyond Simonsen for Burnley's fourth.