Many tribes had rituals for thanking the animals for giving up their lives so others could live.
For either of my tribes this was generally done by the brave who actually killed the animal. It was more "in the manner of what people today would call prayer" in that forgiveness was always asked of the animal.
For the tribe when the carcass was brought in there was a celebration because it meant some or most of the tribe would be eating good tonight.
I remember the look on grandmothers face when a larger animal was brought in even if it meant more work because we would have food for that meal and sometimes a few extras with just one days work.
I have not actually been part of a ritual other than what my grandmother taught me to do alone after I killed an animal.