James Lawton: It's a scandal that Carragher will get away with his assault on Nani

United are in trouble. Whatever happens between now and the season's end, they have to be remade, most urgently in midfield. There, they reeked of decline

This was a brilliant and complete Liverpool victory. It confirmed so many of the hopes raised by Kenny Dalglish on his return to Anfield.

At the same time it was a devastating exposure of the weaknesses that, until the last few days, have lurked not so far below the surface of Manchester United's resilient but often unconvincing challenge for their 12th Premier League title.

Yet, if this important football match bears huge implications, especially for Arsenal – now just three points behind United with a game in hand and with a goal deficit that might be swept away in just one burst of virtuosity – none of it was momentous enough to provide even a wisp of a smokescreen for the scandal that lay at its heart.

At the end of a week of refereeing controversy it was that Jamie Carragher was merely given a yellow card for a tackle on Nani so sickening, so dangerous, that it rendered more farcical than ever the insistence of the football authorities that they cannot revisit extreme cases of negligence, irresponsibility or – let's not fail to explore the full range of possibilities in this case – outright failure of nerve by a match official.

Phil Dowd was close at hand, was surrounded by protesting United players and Liverpool captain Steven Gerrard – who appeared to be suggesting that his team-mate was not guilty of one of the worst fouls to disfigure any ground in recent memory – and then administered two yellow cards, one to Carragher, still protesting his innocence, and the other to Edwin van der Sar, incredulous that a tackle of such crude violence could elicit such a mild punishment.

Sometimes you have to despair of the inability of football to police itself – and of those who watch it to separate their tribal instincts from the evidence of their own eyes.

We had another example of this after an incident that followed hard on the Carragher tackle when Rafael, United's young Brazilian full-back, was yellow-carded for a tackle on Lucas, a moment after the latter's team-mate Maxi Rodriguez had come at him thigh-level.

Rafael was inflamed, no doubt, and his tackle was reckless – but his feet were low, unlike Carragher's, whose boot hit Nani's standing leg shin-high – and Lucas was unscathed. However, this did not prevent Rafael being booed relentlessly through the rest of the match.

Some will say Nani's notoriety in the play-acting department worked against his outrage and that of his team-mates – especially when he got to his feet to join in the protests before falling again – but you didn't have to be a drama critic to detect authenticity in his tears and his shock or, as United's most threatening player, his departure on a stretcher. Sometimes there really is a wolf in the grounds and yesterday his name was Carragher.

This may offend some Merseyside sensitivities – and we all know what a sterling professional Carragher has been down the years – but you had to be living on another planet not to be revolted by this piece of action. Nani wasn't tackled – he was, in effect, assaulted – and we can re-run the film a thousands times without a softening of that verdict.

Certainly it will not do for Dalglish – who was hinting before the game that Sir Alex Ferguson's criticism of officials tends to work in his favour – to offer only this bromide: "It's not correct to talk about incidents because the match was played in a great spirit."

Silence, you have to say, would have been the better option.

Did the absence of Nani have a decisive effect on the outcome? It's not the point but, of course, the answer is plainly no.

If you had drawn up a list of the advantages of Dalglish's appointment – one which will now surely be made permanent – you would have spent most of this match ticking them off. Most striking, of course, is the fact that Liverpool now look like Liverpool again, a team of conviction and self-belief, one capable of growing before your eyes.

In terms of manpower, the differences between the team that finished last season so bedraggled and lurched into this one so unconvincingly is slight enough but the psychological change is huge. Luis Suarez is a player of thrilling nerve and touch and Raul Meireles continues to develop as a force of brimming value.

Dirk Kuyt, who has always been a superior scavenger, surely put down a solid footprint on Dalglish's new Liverpool with a hat-trick that owed everything to his trademark resolve to turn over every stone in pursuit of victory.

United? Five days after crumbling at Chelsea, they again lacked their own Dutch boy to put his finger in the hole in the seawall. No doubt, Ferguson will ransack all his reserves of defiance in an effort to get his wounded team over the line, but, if Arsenal can find some of the resolve that deserted them so profoundly against Birmingham City in the League Cup final and at home to Sunderland, United are clearly in trouble.

Whatever happens between now and the season's end, they have to be re-made, most urgently in the midfield. There, they reeked of decline. Nor does it help that Wayne Rooney appears to be operating from an imperfectly working memory.

It was an inept performance – almost as shocking as that tackle.