It may be a fallacy to assume a neuron is less complex than a brain. Depends on how one measures complexity and at what scale... but living systems -- unlike no living systems -- strangely get more complex the closer in one goes. That is, it's fairly trivial to simulate an earthworm... it's trickier to simulate the components of the earthworm.
This is a completely minor point here... but "fallacy" means that there's something wrong with the argument, if you have a disagreement about facts or assumptions then the word "fallacy" doesn't really apply (you can just say "wrong" instead).
It suffers from the fallacy of petitio principii, in that it assumes arguendo that consciousness is comprised of neurons (and, as mentioned above, that a neuron is less complex than consciousness.)
But it's not stated as an 'argument' in any case so perhaps the term fallacy was out-of-place.
Petitio principii is when the premise assumes the truth of the conclusion, but since there is no argument and no conclusion it's impossible for the statement to suffer from that fallacy.
