I can only say that I've never used my hands to play with any puppy I've had. I've always used toys. I don't want the dog biting even if they are play bites, while we are playing.
I don't mind if the puppy (Lisl in this case) is mouthing my hands with slight pressure while we are just spending time petting or brushing her. She knows when it's too hard and I have to remind her with a little yelp, or saying 'no biting' firmly to her.
The easiest way to get hurt playing with a puppy is using your hands as another dog would use it's mouth and/or paws. An excited puppy and moving jaws with sharp puppy teeth is an accident waiting to happen, as you found out.
I'm not saying it's wrong, I just don't do it.
Bear, Anna, Molly, Ossie, and The Countess Lisl von Schlaf