Quantum effects are crucial for all neural phenomena including learning, attention and memory, which are key aspects of perception and cognition. There is also a vast array of biomolecular entities that exhibit behaviour intermediate between classical and quantum systems (e.g. protein folding, molecular motors, microtubules). Most neurons have several dendritic spines where quantum effects should play out, so we can expect to see quantum mechanical effects emerging from many types of neural activity.
It is certainly true that quantum effects do not extend to macroscopic objects but it’s easy to show that the fundamental biochemical processes that are going on within even the largest synapses (20-100 nanometers) are in principle sensitive to quantum mechanical effects (using chaos theory) . It’s not the number of atoms or macromolecules, since we’re not dealing with individual particles; it’s the collective action of the molecules and atomic forces between them that forms the basis of the argument. Even at the single molecule level, the brain’s chemistry is quantum mechanical. Take a look at this electron micrograph of acetylcholine, the neurotransmitter released by presynaptic terminals onto postsynaptic cells, which triggers the opening of ligand-gated ion channels.