It wasn't death that was introduced, it was the realization that each of us will die. An animal is often repulsed by something dead, but it has no realization that it will die as well. We are the only species that understands this much of our own fate. And it is because of our more well developed intellect that we realize this. Thus, the "apple" from the "tree of knowledge" introduced "death" into the Garden of Eden.
They are also often attracted to something dead because they want to eat it.
True, animals are not able to reflect on death and non-existence the way we do. But they know enough of death to fear it and avoid it when they "smell" death. Such unpleasant feelings (fear, terror, anxiety) by definition cannot be present in paradise.