Everything that has ever existed continues to exist, in one form or another, and as far as we can tell, humanity was more aware of that back then they are now. So the sacrifice, song, praise and prayer did not ensure the immortality of the slaughtered, either in body or in spirit.
That was already taken care of. What it did ensure was the continuance of the connection between the spirit of the slaughterer and the spirit of the slaughtered. Killing is risky business. The membrane separating the internal from the external is not necessarily as thick or as clearly defined as we have come to believe. Every time we kill, we risk killing the reality of that thing inside of ourselves as well as outside. We risk breaking the connections that lead in and out.
Taking life to feed life requires a keen understanding of the natural law of give and take. When humanity lost that understanding, gave up the songs, the sacrifice, the prayers, the praise, they lost the connection. Saying grace is not enough.
When you lose those connections, everything becomes dead - fish, rivers, frogs, mice, even each other. There is no way they can reach inside you any more. The five senses you are left with are not enough. You have given up those connections in exchange for the freedom to clear cut forests with skidders, turn cows into milk machines and chickens into egg factories. You can experiment on animals, club seals, wear mink coats, exterminate passenger pigeons, dodo birds, whales, bear, dolphin and condor with not a twinge of guilt. The lines have been severed. We are under the impression that it is the forests, the creatures, the spirits, and the wildlands that are disappearing from the universe and not we. Not so.