Johnson would've started in place of Jo though, a striker, not Milner a more defensively minded mid. You could argue given his build and physicality, Jo is a better defensive option than Johnson anyway, but that's not what you've said.
I'm very much of the "well, we [Arsenal] played an attacking strategy and were unlucky to hit the post 3 times, but well done to City they defended well and Hart played well" opinion, as you put it, but I don't agree that Mancini executed his plan that well at all, let alone brilliantly. City got a point, in the end, due to a combination of poor officiating - we should have had a pen, and luck - we really should have and easily could have put some of our chances away. Also, Tevez didn't really have a single proper chance that I can think of, so the pump it long to him strategy failed as well. Had the result remained the same but they'd looked defensively solid, I'd be wholeheartedly agreeing that it was a good, if somewhat obvious gameplan, that had been executed well and we'd witnessed a defensive masterpiece, as it stands though, I'm sure City feel lucky to have come away with the result they did, and there's a reason for that.