You do realise man marking is a tactic that is used in every game? Charlton-Beckenbauer in the 60's, Keane-Vieira, Xavi-Pirlo in the 4-0 battering a couple of years ago. Fletcher always used to man mark Lampard when we played Chelsea, there's a few well known examples. You make tactical preferences in order to nullify the opposition, that's just blatantly obvious and if you don't understand such basic aspects of football then it explains why youre completely ignorant to Carricks qualities as a footballer.
In terms of examples, they've already been covered. Carrick comes back, we suddenly stop conceding and start winning games. To reiterate, "you don't understand his influence until he's not there" whys that even a quote? Because the best examples of his defending aren't obvious.
Anyway, the best thing I can present to you is a video Gary Neville does, which is pretty much Carrick for beginners;