There is a little aside here that we should get to before we go past it, but it will not take long. When these verses are combined with Genesis 1:28-29 and Genesis 4:1-5, it shows that this is not mankind's introduction into eating animal flesh. You can read verse 3 in chapter 9. But in Genesis 1, what God is doing is showing that all life, animal and human, ultimately depends on vegetation: I have given you all the green herbs to eat. And that is true.
Remember Genesis 4:1-5. Abel brought to God an animal sacrifice. That shows us that God had already showed them that their dominion over animals extended to the place that they were able to take an animal's life. God was well pleased with Abel's animal sacrifice. He was so well pleased that it is recorded back in Hebrews 11 that it still witnesses. So God was not overly concerned about the killing of an animal, but what we need to understand is that they understood about sacrificing, and some of the sacrifices had to be eaten. That was a requirement of God. The sin offering was to be eaten, part of it anyway, and the peace offering was to be eaten.