Yes it's a slip, but that's still followed up with enough conscious grappling that it's a definite missed foul. And let's not forget, he didn't give the foul and then bottle the card (which is what would match your concept of game management) - he looked directly at it and pretended there was no foul there, because he knew it was a mandatory yellow if he gave the foul. Liverpool weren't given the opportunity to make anything of it, because the game continued and the ball was booted away!
Had United gone on to draw or win the game, it probably would have ended Liverpool's chances of getting into the CL next season - and at that point, I believe the game was at 3-2. I'm sorry, but I'm not prepared to accept the idea that referees should be able to make laws up when they affect things of that importance and with that much money behind it. Everyone on here quite rightly hated the idea of the ESL, but when Liverpool's fate can end up being in the hands of a referee who's making it up as he goes along, you can suddenly have some sympathy with owners who aren't prepared to risk their club's finances on that kind of nonsense!
And that last bit about the rating of AT wasn't specifically directed at you, but it is well established that the FA prefers AT. There are a lot of very credible theories surrounding the lack of English referees at the 2018 WC being because the FA preferred AT where FIFA preferred MO, and they constantly get similar-profile matches where for me MO is clearly the better referee.