Yes, it's shock. Don't worry, it happens to everybody - horrible as it feels, it's natural and everyone who's suffered a close bereavements will understand. Have you got 'white noise in your head'? Lasts for weeks. No, you can't concentrate while that's going on - it's something your mind does to shut you up while it processes the news.
When a parent dies, your whole personal landscape has changed for good, hasn't it? Quite suddenly as a rule. My dad was an arse of the lower orders, but he was a defining feature in all of my life and who I was. The shock & grief were just the same.
Don't drink much alcohol - it won't change anything, only delay your recovery. Do talk to other people who've experienced it. Do try & stay in touch with the everyday world: most people will understand that you might be a bit quiet and have to leave early. Don't force yourself to accept challenges! You're challenged enough as it is - get compassionate leave from work (if you have an employer) and use a sick note or holiday to extend it, if you feel the need. Do eat! Anything's better than nothing, and do drink plenty of water.
You're not over the first shock until the 'noise' stops. It will take up to two years to actually come to terms with the whole grief thing; you'll just find it happens as you go along.
Be gentle on yourself, and require those close to you to give you plenty of space. You're not alone, though I bet you feel it. Thinking of you.