Possible to feel the nerves on a tooth removed from your mouth?

I know it doesn't make any physical sense, but once when I was little I touched the bottom tip of a tooth that came out of my mouth an instant after it came out and I felt a shooting sensation in my gum in the same instant. Is there any way that was possible? It seems with no axon/dendrite physical chain connection it wouldn't be, but I distinctly remember it happening.