You'll get used to it, every tier change takes a while to get used to.
With faster greens, as Apex has already said you don't need to hit the ball quite so hard. This also means you have to allow more for side slopes as a slower moving ball will move more off line than one given a good whack.
If you find yourself struggling with short putts, 2-3 feet, then try aiming just inside the hole on the high side and hitting the ball hard, at least 2-3 feet too strong. It's nerve wracking at first but I find it easier than dribbling the ball in. There is a risk you'll have a longer return putt if you miss of course, confidence is important. And I wouldn't necessarily try it if there is a severe break, across BPB #15 with the pin cut at the front for example.