That's the problem - I don't know a strict and correct definition for it, not even close one. At minimum there are two polar possibilities - 1) any neuron firing due to damage is a "feeling of pain", or 2) only conscious brain can "feel pain". But there can be other definitions, multiple ones.

First option is possible but not productive for the discussion because then almost everything can feel pain, including some single cell organisms I think.

Second option is anthropocentric and at least at a glance looks incorrect.

The thing is the word "feel" itself is anthropocentric, basically we make analogue with our understanding of pain and project it on other living organisms.