Dennett doesn't dismiss the difficulty of the problem, he just dismisses that the difficulty is where people think it is. For instance, he would fully agree that the brain is insanely complex and just elaborating how information processing works will be very, very challenging. His opponents then say from this position of ignorance on how this works, "but even if you explain all of this, there's still something left to explain!"
Is there really though? How could they possibly know this? It's a classic god of the gaps argument/argument from ignorance that theists use to cling to their deities or support intelligent design, hence "residual christianity". After all of this time debating consciousness, the very best arguments we have for qualia that cannot be captured mechanistically are thought experiments that are easily dismissed as circular (and which Dennett has ably deconstructed to show their vacuousness).
Frankly, I find Dennett's rebuttals are brutally logical and pragmatic.