We only see a very limited spectrum of light, but we don't realize the massive gaps we cannot see. All of our senses are a tiny pinhole into the world, and we base our reality on them. Our sense of smell is a fraction of other mammals, we really don't notice that a dog could be smelling 20 things in a room that we don't notice.
Not that we really have any other option, but I am just trying to explain the 'illusion' of it.
On the other hand, the physical world exists, or at least out perception of it exists. You might say that you also perceive consciousness, but honestly, what is it you perceive? I don't think it is the same as perceptions of physical things.
What is it that people say distinguishes conscious things from non conscious things? Consciousness is affected by what other things are, vs only being affected by how other things interact with it. For example, given the right momentum, area, and angle of impact, one lump of matter has exactly the same effect on my red bouncy ball as any other lump of matter. The kind of object the lump of matter is makes no difference. On the other hand, the kind of object has a very definite effect on consciousness, more so than the material make up. This paragraph can be embedded in any kind of medium that you can read, and the medium makes no significant difference in the effect of the paragraph on your consciousness.
Does that kind of distinction seem coherent to you?
People have this notion that there should be this something called consciousness, but they can not say what it is supposed to be. This becomes especially clear in Searle's Chinese Room where Searle describes how an intelligent process is supposedly not conscious, but he still dodges the question what he means by consciousness. To me the chinese room shows that there is no such thing (ie the notion seems to be that a human speaking chinese does so by employing his "consciousness", whereas the chinese room example basically proves that consciousness is not required).
"How do Newtonian physics, quantum physics, and relativity work together? Don't worry about it, the physical world is just an illusion, and illusions aren't rational."