Thanks for trusting this community with your feelings, Lilly.
Firstly, I'm sorry to hear that you've recently lost your father.
What you're describing is perfectly normal. You're not missing any part of your brain or consciousness or anything of the sort. This is not an inability on your part, it's simply one of the ways that we've evolved as a mechanism to deal with loss. (There's a good look at what grief is and how it's often expressed
here.)
Some people completely fall apart. Some turn to drugs and/or alcohol. Some become wildly horny (yes, really... sounds odd, I know). Others don't give it a second thought and brush it aside.
When - and if - it becomes time to cry, you will cry. But if you don't, that doesn't mean you're deficient in some way, it just means that your body and mind deal with the loss in a different manner.
So relax. Chill. Here, have a nice Guwerztraminer.