Depending on what kind (size esp.) of snakes you keep- you for sure need to slow down & pay attention to their body language, & do your best to prevent such bites. We always remind people not to jerk their hand away, but I know that's pretty hard advice to follow- reflexively we do it anyway, most of us. I'm guessing that's why yours was so deep?
Forgot to clarify, the bite was from the puppy.
Zebes has yet to ever bite me, and I've gotten very attuned to reading his behavior to the point where I can tell if he's stressed about something so I'm learning well there.