I would say yes of course the brain is the source of consciousness. However, the functions of the brain give rise to more than just firing neurons, it gives rise to complex systems and effects that are more than just their physical source. Take a computer, for instance. The most basic part of a computer is the mechanism that makes a byte turn on or turn off (binary). This gives rise to all sorts of things, such as calculations, visual output, etc.
With the brain, it is even more so. It has the same function as bytes in a computer (for a neuron to fire or not to fire), yet it is capable of consciousness, something absolutely amazing that has not been copied by any computer yet.
Part of consciousness, though, has to involve what Sartre called neantation or nihlation. It must be, as I mentioned before, a clearing or eregnis. Otherwise, matter would be indistinguishable from consciousness, and we would only be able concern ourselves with what exists in the moment, and be incapable of imagination.
Imagination requires, as Sartre said, a double nihlation. First, it must withdraw from the world (hence needing something that is separate from matter) and then taking an object that is not, and imagining a world in which it exists. This is imagination, at least, in its most basic form. I would say that the higher processes of consciousness come about from the basic physical actions of neurons, creating a sort of metaphysical essence that is consciousness. Consciousness must "be in the world," but not "in the midst of the world," otherwise it would be undistinguishable from matter.