There was hope for both managers after today's match.
For Brendan Rodgers there are clear signs that Liverpool are on the mend. If he had started with a braver formation, they might have got something out of the match.
For Sir Alex, the defence was as sound as it has been this season. OK so Liverpool scored, but sometimes you have to give credit to the opposition. If you were picky, Sturridge should have been followed by Rafael, but it was a well-engineered opportunity with a clinical finish.
But what will have pleased him most is how much United dominated the first half. This was as much as anything down to a Carrick performance as good as he has had this season.
Contenders for key man
Gary Neville awarded "Man of the Match" to Danny Welbeck, which must have been for sheer endeavour, because he failed to score from the several chances he had.
In truth the key man was the whole team, because there wasn't a single player on the United side who didn't work his socks off and make a decent contribution.
For all those who thought United's biggest problem was their leaky defence, there wasn't a player among them who didn't do the business.
No doubt as soon as it was announced that Evans had dropped out with a hamstring, there were those who feared that the Vidic/Ferdinand partnership would be undone by Suarez. In fact, Ferdinand was excellent, and in truth there wasn't really a goal threat until Sturridge came on.
Vidic was also excellent at organising the whole team, and Ferdinand was calm and composed.
But the real stars at the back were the two wide men. Evra was back to his very best, although unable to get forward as much as usual. Apart from the header that resulted in the goal, he was sound in defence, which has been his Achilles heel in the last year or so.
Meanwhile, Rafael showed why Sir Alex has invested so much belief in him. He has learned to stay on his feet, and from a cavalier young man who loved to fly forward, he has become a fine defender as well. He was simply outstanding apart from the slight aberration for Liverpool's goal.
Between them, Evra and Rafael ensured that any threat from the wings or wing backs was nullified. Raheem Sterling was largely anonymous until he was substituted. Downing did better but was shepherded onto his weaker foot all match.
The truth of the matter is, however, that this match was, as expected, won and lost in midfield.
It was expected to be a "blood and thunder" match, which it became more and more, as it progressed. Liverpool's game was also expected to be about "passing and pressing." Actually it ultimately distilled down to the difference between the two midfields.
Liverpool started with Lucas and Allen in the middle, United with Carrick and Cleverley, which is now beyond doubt their best combination. If anybody had any doubts, then a 56-percent possession stat for the whole match is the best evidence.
Brendan Rodgers has raved about Joe Allen, describing him as a "unique and frightening talent" when signing him for £15 million.
To be frank, comparing him on the day to Michael Carrick was like comparing boy to man. Allen could learn a lot from Carrick. Both are unassuming professionals, but Allen looked lost in Liverpool's midfield, whereas Carrick seemed to cover every blade of grass.
Surely he is having his best season ever, and United's fortunes will hinge on his ability to stay fit.
Winning over the doubters
Carrick is finally getting the credit he deserves, but there will still be people ready to jump on the slightest mistake.
It is natural to compare him to Paul Scholes, even though they are very different players playing very different roles. Carrick has now emerged from the shadows of his illustrious fellow teammate to show himself to be a more complete player.
Even taking the most demanding definition of an interception, Carrick made at least 14 today. He also put in three crunching tackles, all of which resulted in a free kick; all stopped Liverpool's momentum; and none was remotely approaching Scholes' "X-rated" efforts.
The true comparison on the day should have been made with Steven Gerrard. He was playing "in the hole" until Lucas was removed but he was what he has always been to Liverpool, the leader and driver.
Carrick didn't lose the ball once for 68 minutes. There are always those who hate him, who bemoan all the "sideways and backwards" passes, or will shout blue murder at the slightest error or dalliance.
Those are the one-eyed critics who would blame Carrick for Liverpool's goal. Wrong. It was Cleverley's "hospital pass" that Gerrard saw coming a mile off, intercepted and set up the goal.
Nobody will have covered more ground than Carrick, and supported by the equally unassuming Cleverley, they ran the midfield in the first half. As a result, Suarez had to come deeper and deeper, and Liverpool had only one "goal attempt" (to give a loose description) in the first half.
So Robin van Persie scored one and made one. Danny Welbeck ran his socks off to get "Man of the Match" despite failing to add his dismal return of one goal this season.
But the watching Roy Hodgson will have seen what England have been missing for years in preferring Gerrard and Lampard to Carrick and Scholes.
He is a tireless, calm, competent workhorse; the English Pirlo; he can read the game and breaks up attacks time and again; he plays the sort of incisive through pass that Scholes has always revelled in, but intercepts and tackles in a way that the latter has hardly ever done.
Oh and by the way. Luis Suarez was faultless, staying on his feet when he could easily have gone down in the penalty area towards the end of the match. He shook Evra's hand and even politely collected the ball and handed it to De Gea for a goal kick.
If he was like this all the time, we might all get to like him...