Exactly. They can give the impression that they feel pain, but so do characters in video games when you "smack 'em" or shoot 'em. But they don't really.
I believe the animals brain is quite aware of what is stimulating his nervous system and responds with a pre-programmed response. I also believe animals can "learn". But I do not believe they "feel" in the way we apply the word to humans. They "feel" like you car "feels" when the check engine light comes on. It is a pre-programmed response originating from the brain (cpu) in response to an electrical impulse from a sensor (nerve ending), and that is all.
It would be unnerving if every time your check engine light came on, part of the programming cased a digitally stored recording of a womans blood curdling scream to come over the stereo speaker system. But it wouldn't really mean your car felt anything.
If that is how you'd define the mechanism whereby an animal senses and can respond to the stimulation, how is it different in a human?
That's probably about how a large predator assesses the responses of a human as it rips out the first big bite. "I bite food, it makes a loud noise, so what?" Most humans, excepting you apparently, are better able to comprehend what another sentient creature is feeling. Animals, like very young humans, don't appear to be able to "put themselves in another's shoes", and consider what it must feel like to be that other creature in the given circumstances. But, also like very young humans, this does not mean they aren't feeling anything themselves. A 2 year old human which hits or bites its newborn sibling out of instinctive jealousy, doesn't grasp that it is causing the little creature pain, but torture the same 2 year old and s/he he will definitely experience agony.