Generally speaking sacrificed animals were still eaten, though certain parts might be burned completely.
The good meat was normally eaten by humans after sacrifices, not wasted.
A sacrifice was normally a loss only for the owner of the animals, if after being sacrificed in a public ceremony their remains were shared with everybody in the community, instead of being sold or consumed only in the house of the owner.
(To my understanding, giving the god(s) only the "undesirable" parts of the animal is popularly associated with the Greek gods, not Abrahamic faiths.)