Areas that Michael Carrick has to improve are decreasing the quality of shots Manchester United conceded under Ruben Amorim and Darren Fletcher by defending and attacking well.
He hinted at that after the Man City game as he wanted close distances between positions & units while operating off-ball.
And the Manchester Derby was one of the few games — if not the only game — in which the goalkeeper didn't face well-placed shots and wasn't forced to make extraordinary saves.
For Manchester City, I think it's the same case as Real Madrid. Despite their subpar out-of-possession approach and rest defense, opponents are capable of accessing high-quality scoring areas; however, they underperform by taking low-quality shots, and Donnarumma being a God-level shot stopper (the Manchester Derby is a prime example).
For Liverpool, it's a mix of opponents' ability to find inroads and create situations where shots are quite difficult to save, GKs brilliance, Arne Slot going to low/mid-blocks more often, and passive high press.