Disgust against child sacrifice and most human sacrifice was a Roman sensibility, long before there was any church or christianity.
On the whole, the Romans were quite enlightened compared to the other brutal civilizations of the ancient world, being governed more by law than superstition, but they still had these quirks that wouldn't be eradicated till Christianity replaced the state religion.
It's not the killings of prisoners themselves - those were common throughout the ancient world, alongside slavery. It's the fact that they killed them at the temple to the chief god.
I'd define anything as human sacrifice that the culture performing the act would label thus. E.g. we, as a modern civilization, don't call an abortion, war or execution "human sacrifice", so it isn't. The Romans didn't consider executing prisoners as such, because the prisoners were just subhuman and it was just an execution, so it isn't. The Carthagians seemed to think they were doing a human sacrifice, so yes, they were.
I'm not talking about car (or chariot?) accidents here, I'm talking about literally thousands of people being executed on the grounds of a temple dedicated to Rome's chief god. Certainly people died in the Circus Maximus, and that is just sporting accident. I wouldn't even call gladiatorial combat human sacrifice, since it was mostly an entertainment spectacle in a more brutal time.
We're talking about Romans taking prisoners captured in war, marching them to one of the most significant religious locations within the sacred boundaries of the city, and executing them.
My issue with just trusting the ancients is that they sometimes aren't trustworthy. It's very possible that Rome didn't admit this was human sacrifice because Roman culture condemned human sacrifice, and kind of turned a blind eye to the ethics of this ritual.
The Romans did this through the ritual of immolation, where the animal was marked as a sacrifice by spreading mola (wheat spelt) and salsa (salt) on it. No immolation, no sacrifice. If they killed someone without immolation, to them it didn't have the purpose of pleasing the gods and thus wasn't human sacrifice. Edit: "immolation" in this context might be somewhat different in the english meaning. See https://en.wikipedia.org/wiki/Mola_salsa for what I mean.
A lot of religions (don't know about the Roman in that aspect) also frown upon the intent of a sacrifice being impure: If you do the sacrifice with more than just the goal of pleasing God, e.g. to additionally get rid of that obnoxious goat/cock/person/..., then God won't be pleased.