Ross Flitney had advanced a few yards out of his area as Barnet pushed forward but when United countered, the hapless goalkeeper got his measurements all wrong and plucked a routine pass forward out of the air under no pressure at all a yard before the ball had gone back into the area.
If ever there was a case for referees being allowed to use discretion in administering the game, this was it.
Virtually to a man, the 43,673 crowd - the lowest at Old Trafford for six years - disapproved of Beeby's decision to reach into his pocket with a shrug and wave the red card in Flitney's face.
After spending so long looking forward to a day he should have been able to remember with fondness forever, Flitney was inconsolable as he headed to the dressing room.
Spare a thought too for striker Louis Soares, the man sacrificed for the introduction of Flitney's replacement Scott Tynan, substituted without even kicking a ball.
To make matters worse, Liam Miller, a man who definitely had something to prove, exacted even further punishment by superbly curling the free-kick into the top corner.
Even Sir Alex Ferguson was probably shaking his head at the injustice of it all, but the unexpected development at least allowed his young side to give free rein to their talents.
As usual on these occasions, Ferguson had packed his side with youngsters. Three 18-year-olds, two 19-year-olds and a couple of 20-year-olds represented one of the most inexperienced United sides ever seen, in which Adam Eckersley and Richie Jones were handed their debuts.
It was also the first chance many Red Devils supporters had to cast their eye over Lee Martin, the England youth international whose promise persuaded Ferguson to commit #1million to luring him north from Wimbledon as a 16-year-old.
Martin's development has continued during the intervening two seasons and the Taunton-born teenager revelled in the extra space he found on the right wing even if his night was eventually to come to an unhappy end.
Equally impressive was Eckersley, whose darts forward from left-back were a constant source of menace to the Barnet defence.
Given he is now an England international, Kieran Richardson probably should have stood out against 10 men from a lower league. And, pushed into midfield, he duly did.
After bringing a superb save from Tynan not long after Miller had opened United's account, Richardson went on to double United's lead, although the effort had an element of freakishness to it, a touchline free-kick which floated across the box and into the far corner with no-one getting near it.
By that time, a close-range Giuliano Grazioli effort had been ruled out for offside, so Fairclough and his side presumably knew it was not going to be their night.
At least Tynan was enjoying himself as the man who expected to spend the night watching emerged as the main barrier to United recording a landslide victory.
On at least five occasions, Tynan came to his side's rescue, with Sylvain Ebanks-Blake the man most often denied.
There was nothing Tynan could do to stop Giuseppe Rossi making it three though.
Of all the youngsters on United's books, the US-born Italian has the most glowing reputation, having followed up his free-scoring season at reserve-team level last term with his first senior strike at Sunderland earlier this month.
And although he had wasted a couple of decent chances earlier, when Martin cut a cross back five minutes after the break, Rossi fired into the corner with clinical efficiency.
It proved to be Martin's last meaningful involvement before he was stretchered off in extreme discomfort after crashing into an advertising hoarding.
Dean Sinclair did bring the visiting fans to life late on when he seized on Gerard Pique's blunder and fired home.
But the final word went to United, and Ebanks-Blake, who nipped in after Rossi had knocked Miller's long ball into his path, swerved round Tynan and tapped into the empty net.
Barnet boss Paul Fairclough blasted the `cruel' decision to send off goalkeeper Ross Flitney 100 seconds into the 4-1 Carling Cup defeat by Manchester United.
Flitney was guilty of a major misjudgement when he caught a bouncing ball under no pressure a yard outside his own area.
Referee Richard Beeby felt he had no alternative other than to show Flitney a red card, leaving the young keeper to head for the dressing room in tears.
The ruling also had a knock-on effect for striker Louie Soares, who was substituted without kicking a ball as Fairclough was forced to call on replacement keeper Scott Tynan as well as ending any realistic hope Barnet had of landing a shock win.
'It was a really cruel decision,' said Fairclough.
'It ruined two players' nights. We all talk about the problems football has but there has got to be some soul and heart in the game.
'It wasn't malicious and Ross wasn't seeking to gain an advantage, it was just an error of judgement, surely a yellow card would have been enough.
'The lad was distraught, really distraught and we have also had to take off young Louie, who had not touched the ball and, like us all, had been looking forward to this night ever since the draw was made.'
Even Sir Alex Ferguson admitted the ruling was `harsh, really, really harsh' and felt it had done his young side no favours despite the comfortable margin of victory.
Flitney's former Fulham team-mate and current United number one Edwin van der Sar left his seat in the stand to comfort the Barnet man at half-time.
'Surely we need some common sense,' said Ferguson. 'Everyone was stunned by it. It shattered a young boy's dream.'
To compound Barnet's misery, Liam Miller promptly curled home the free-kick, setting United on the road to an easy win.
Kieran Richardson doubled the lead before the break, then Giuseppe Rossi enhanced his blossoming reputation with a clinical finish after the interval.
It was the USA-born Italian's second goal in just four senior appearances for the Red Devils and Ferguson has high hopes for the diminutive 18-year-old frontman.
'Giuseppe is a natural footballer,' said the United boss.
'He has an excellent awareness of space and is a marvellous finisher. He has a big future in the game.'
Dean Sinclair put some gloss on an otherwise miserable night for the visitors with a consolation effort, although it was a United side containing five teenagers who had the final word when Sylvan Ebanks-Blake, who only broke his leg in May, took Rossi's lay-off in his stride and tapped home a fourth.
'We feel fully justified in persevering with the principle we have of playing young players in this competition,' said Ferguson.
'Everyone associated with Manchester United finds something refreshing about producing our own players.
'We have brought a lot through and hopefully that trend will continue.'
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