At least Manchester United have got their defence of the Carabao Cup to concentrate on this week. They should put all their resources into their fourth round tie against Newcastle United on Wednesday because, frankly, the most prestigious silverware in English football remains out of their reach. Way out of their reach.

An afternoo that began with a beautifully moving tribute to Sir Bobby Charlton and an evocation of past glories at Old Trafford turned into another sobering lesson at the hands of Manchester City, whose majestic dominance over their local rivals in the last decade has been a constant reminder of how far United have fallen.

The stark truth is that United do not appear to be getting any closer to Pep Guardiola’s champions. They were outclassed here. Long before the end of a match that City won 3-0 at a canter, United were chasing shadows. City toyed with them. We can argue about whether it was a humiliation but it was certainly a harsh lesson in the art of football.

City’s fans, who had joined in respectfully with the minute’s applause for Charlton before the kick-off, enjoyed themselves more and more the longer the match wore on. ‘Old Trafford is falling down,’ they sang over and over again. Literally and metaphorically, they have a point.

The result moved City up to third, two points off the top of the table, and left United marooned in eighth place. It does not feel like a false position. They worrying thing for the fans and for their manager, Erik ten Hag, is not just that progress appears to have stalled – the team is going backwards.

United are struggling to locate an identity. One of their new signings, Sofyan Amrabat, was hooked at half time. Another, Rasmus Hojlund, was substituted to a chorus of boos in the second half. Another, Mason Mount, failed to make any impression when he came on at half time.

There are other worrying signs of stasis. Raphael Varane was not trusted to start the game even though he was fit. Harry Maguire and Jonny Evans were the first choice centre backs. The previous time Evans had started at home in a Manchester derby, was in October 2011 when United were famously thrashed 6-1. Some things change, some remain the same.

Questions are starting to be asked about whether Erik Ten Hag is the man to take United forwards. The truth is that at the moment, he does not appear to have any answers to those questions. United are atrophying and when Sir Jim Ratcliffe takes charge of United’s football operations, Ten Hag’s position is likely to come under real pressure for the first time.

Ten Hag has some credit in the bank after the improvements of last season but that credit is ebbing away. There is also an acceptance that he had a hell of a mess to sort out when he arrived but the uncomfortable truth is that the men he has brought to the club do not appear to have improved it.

Antony made a cameo appearance and spent most of it looking as if he was trying to get himself sent off. Ten Hag made Bruno Fernandes captain but the only metric in which he leads this team is in the volume of his complaints to the referee. He is, demonstrably, not a leader.

City, in contrast, played like a team who remain favourites to make history by winning their fourth league title in a row this season. They played some breathtaking football. Haaland got their first with a penalty. His second finished off a wonderful team move. He laid on the third for Phil Foden and then ushered him theatrically towards the corner flag for his celebration.

They are at a different level to United in almost every way. ‘The difference between the two clubs is absolutely massive on the football pitch,’ former England player Chris Waddle said.

‘City have been better in every department.’

United hit back straight away. Rodri floated a diagonal ball to the back post, Walker nodded it back, Foden powered a header towards goal and Andre Onana parried it. It seemed Haaland was going to prod it over the line but Onana clawed it away from him and Maguire put the ball behind for a corner.

Despite the worst fears of their supporters, United were holding their own until midway through the half when referee Paul Tierney called a halt to play to respond to a VAR check after City players had claimed Rodri had been held back by Hojlund as he ran into the area at a free kick.

The incident looked relatively innocuous compared to some of the grappling that decorates penalty areas but Mr Tierney returned from the monitor and pointed to the spot. Haaland sent Onana the wrong way from the spot and wheeled away to celebrate in front of the Stretford End.

United looked mystified and horrified by the decision. City nearly gave them a way back into the game when Foden misplaced a pass that put Hojlund clean through on goal. He took the ball around Ederson but too wide to shoot. He laid it back to Fernandes who blasted it over the bar.

Grealish sat Amrabat down on his backside with a body swerve in the closing minutes of the first half as the game heated up but City were grateful to Ederson for a superb reaction save on the stroke of the interval that kept out a ferociously hit shot from Hojlund.

If that was a good save, Onana emulated it a minute later when Haaland rose unmarked in the box six yards out and put everything into a header that looked as if it would burst the back of the net. Onana flung himself across goal and produced a magnificent save to beat the header away.

Neither he nor his United team had any answer to City four minutes after the interval, though. Julian Alvarez spread the ball wide to Grealish, Grealish played a ball inside the full back to Bernardo Silva on the overlap and Silva crossed to the back post where Haaland was lurking.

The league’s most prolific striker had been left in glorious isolation once again and this time he made no mistake. As Onana scrambled across his line, Haaland directed his header back across goal and into the roof of the net from six yards out. From start to finish, the goal was a beautiful piece of performance art.

City were painting pretty pictures all over City’s penalty area now, a dummy by Bernardo Silva, a one-two between Haaland and Alvarez, a cross-shot from Grealish that flew just wide. There was a sense of City pulling away from their opponents. It began to feel as if they were toying with United.

When United did create a chance to force their way back into the game, they wasted it. Midway through the half, Eriksen guided a brilliant long ball behind the defence and on to the chest of Rashford. Rashford took it down and waited for it to drop but when it did, he dragged his shot wide.

United know they have to take chances like that to have any chance of competing with City when City’s approach play is so clearly superior. United have to be ruthless with their finishing but that is a skill which eludes them too often.

City rarely suffer from that weakness and ten minutes from time, they put the match beyond reach. It was beyond reach anyway, really, but the third goal confirmed it. When Onana could only push away a drive from Rodri, Haaland retrieved the rebound and played it calmly into the path of Foden, who tapped it in.