I used to buy dead baby mice to feed my Burmese Python, but the shop would sometimes run out when it needed feeding so I would by live baby hamsters, gerbils, mice, basically anything it would eat.
The zoo isn't feeding pets to the carnivores, it feeds dead animals that were pets but are no longer.
Once something is dead you don't need to care about it's body, this goes for humans as well as pets.
I would have been fine with feeding my dead parents to lions if it would help the lions. I had no need for their bodies once they were dead and they definitely didn't! Would have been cheaper than the sodding cremations and the stupid "service" we had to sit through.