When you do something wrong, you want to make amends. Make up for it. Make things right again. Atone. Redeem. The sacrifice was a physical ritual showing this contrition. It wasn't to appease God (in fact, it is said over and over again in the OT that God hates those types of sacrifices). It was to show contrition. It's like saying, "Here's an animal that is vital to my livelihood, but it's the least I can give. I love you so much I am sacrificing my livelihood for you." It's the thought that counts. A gesture.
When Jesus came, it was as if he was saying, "I love you so much, I will sacrifice MYSELF for you." He became the lamb. That's what sacrifice is. It's an act of selflessness. He didn't sacrifice himself to somehow appease God - he sacrificed himself for us. He gave his life, so that we may live.
The pagans on the other hand, sacrificed not as a gesture of love or contrition, but in order to appease the gods. This was not good. And really it wasn't a sacrifice at all. They would force people to sacrifice - even their babies - it was purely transactional.
Judaism flipped the script on the pagan world as the Hebrew's were taught that sacrifice was as an act of selflessness, i.e. I will sacrifice something important to me for you, because I love you.