It is thought that fish cannot feel pain because they lack a neocortex in the brain.

This appears to be an older discussion, but since it has come back up recently and is an interesting topic, I will add my thoughts. I would suggest that although biological mechanisms of pain perception may differ across taxa, learned responses to prevent, escape, and avoid painful stimuli are consistent enough to conclude that most species have a functional ability to sense and respond to pain. Even "lower organisms" such as insects, fish and frogs will alter their behavior in response to painful stimuli in a manner similar to mammals. Behavior changes go far beyond a simple reflex, even trending into somewhat cognitive topics such as learned helplessness. You may find a great deal on this topic by doing research on aversive operant conditioning. Punishment, escape, and avoidance conditioning often use shock as an aversive stimuli, and many species develop learned behaviors in response to shock. For a few examples you can see learned helplessness in bees (one of my papers):

Article Studies of Learned Helplessness in Honey Bees (Apis mellifer...

A study on shock avoidance in goldfish and trout (found from a quick google scholar search): https://www.sciencedirect.com/science/article/abs/pii/S0168159105001802

Locating similar literature for reptiles and amphibians is more challenging, as these taxa are less common in learning research. While there are a few papers indicating they have similar ability to learn, I am not familiar with many that use aversive stimuli that would clearly fit the "painful stimulus" category. I was able to find one from 1970: https://psycnet.apa.org/record/1970-03376-001