Conscious experience, the evidence tells us, is shaped, formed and generated by brain activity, and does not occur though the activity of any other structure. If conscious experience is a property of neural activity, it is a specific property of neural activity, as such it does not have the same attributes and features of other properties, the intricate geometric shapes of snowflakes, or whatever, but it is still a property of certain forms of neural activity.
Conscious experience is probably a unique property, perhaps Earth being the only place in the Galaxy, or even the Universe, where it has evolved from biological processes.
Imagine 6 wedges cut from an orange. When you put the wedges together, a spherical property emerges. To analogize this to the brain, imagine 6 wedges of an orange again, when the wedges are put together, a spherical property emerges, but an apple emerges too.
That doesn't follow. The brain is an extremely complex information processor that has somehow, through millions of years, evolved the ability to form mental representations, constantly updated imagery of the environment along with the associated thoughts and feelings, motor response, etc.
Just because we (the brain itself) does not know how it is done, that this is an unrelated thing that somehow, unexpectedly, appears. It is quite mind boggling, but not because of the reason you gave.
This is exactly similar to the brain. Cells/tissues form the structure and functional properties (analogous to the spherical orange), but then something else above and beyond the usual structural properties emerges, the consciousness. Where did the consciousness/apple come from!?
That statement vastly underestimates the complexity and information processing power of a brain.