Kaiser Khronos
I'm not very empathetic either. I've had three relatives pass away within two years. Didn't cry at any of their funerals or subsequent family gatherings. I felt sad but it was a "meh, I'll get over it" kinda thing.
Maybe its because I'm EXTREMELY introverted. I only ever had a handful of friends growing up, went to school in a different city than I lived (about 15 miles away) and I've never had a girlfriend. I only ever get emotional from TV and movies. I remember whenever Toystory 3 was coming out, that Disney released 1 and 2 in 3D. When I went, I actually shed some tears during some of the songs. I'm more empathetic towards fictional characters because, as the movies establish, you know EXACTLY what makes them tick. People are complicated.
Your description is not anywhere close to a lack of empathy. Rather, you're simply displaying a lack of strong emotion or you're repressing strong emotion, which is not at all as large an issue as a lack of empathy. This may be due to your not having a strong bond with those relatives.
An example of this would be myself. I can be very empathetic, however, I displayed a lack of emotion at my grandmother's funeral. I was not even slightly sad. I was, in fact, immensely bored with the subject and was wondering if it were going to rain, then had a mental discussion on media and its insistence at making funeral/misc sad scenes be in the rain, and then debated within myself why anyone would think rain is sad even though it is what makes things grow. Then I noticed everyone was crying and wondered why people cry at funerals when they aren't the ones who are dead. I obviously know of grief and I myself have grieved over a loss of someone I had shared a bond with, I simply wondered why it appeared to be the social convention to cry at funerals when I myself preferred to keep my emotions private.