When your fog of grief has a chance to lift a little, you will begin to feel your parents with you, I believe. I don't know of your faith. But my thoughts are that God would not give us people to love so so dearly, only to be taken from them by death. We are the ones that suffer the sadness. They still enjoy our company.
I've had both experiences. My Mother died in an instant, totally out of the blue - a discecting aorta. My Father had many health problems, almost died several times and went on to outlive my Mother 2 years. There is no good way to experience the loss. Prepared or unprepared (and it's sound like you really had no time to prepare for this). Give yourself time. There is no wrong way to grieve right now.
Much like this forum gives all of us valvers comfort in knowing there are others that understand - know also that there are so many of us that understand this type of pain.
My prayers are with you,
Karlynn