I think mental disposition is a huge component of perceiving pain, and it can be entirely sub-conscious. I can't speak for your case of course, but perhaps you were "ready" for the pain in your finger and what is to come and thus the panic inducing element was gone. You could be almost just an observer of the pain rather than the subject.

Fear of the pain can make things much-much worse. If that fear is removed, you won half the battle.

Of course, there are levels of pain where all of the above goes out the window and it is absolutely debilitating, but maybe that's the 13/10 pain level that hopefully most of us never have to experience.