This, anyone here who has ever been hurt bad enough knows how powerful adrenaline is. Wounds become nearly painless, and you just shake a little.
A couple of years ago, a table saw was compelled by my foolishness to take a sizable bite out of my left forefinger. Immediately after the event I was able to take stock of the situation, shut off the table saw, evaluate the extent of the damage, make my way to the sink to wash my wound and apply pressure and a cloth to slow the bleeding. It was not until I had nearly arrived at the hospital that the pain was sufficient to cloud my judgement.
So yeah, you can never count on pain to incapacitate someone. The best bet to stop a threat is to cause massive blood loss which will lead to unconsciousness.