Not everyone has experience with death at that age. I definitely don't think that you didn't care. You clearly loved him, and he was important to you. Sometimes when you haven't dealt with it before, it's hard to understand someone being there but being "gone." That feeling is strange, overwhelming, and scary. There isn't any single best way that you're supposed to behave. Everyone deals with situations like this differently. It doesn't mean that you were "dead inside."

I don't think anyone, especially your therapist, would hold any of these thoughts or feelings against you.