Harris would argue that even that capacity for self-reflection is just part of a very long causal chain. Every thought you have emerges from somewhere, but it's very hard to find the cause of that thought. You might be able to pin down that "I was thinking X because I was reminded by Y," but that just begs the question, why were you reminded by Y? There are an infinite number of thoughts you could have been having at that moment, but for some inscrutable reason Y bubbled to the surface.

All that said, though I think free will is an illusion, in terms of day to day life it's more practical to act as if you have free will. I believe Sam Harris agrees. He is more concerned about the public policy implications, such as incarceration and rehabilitation.