I was just thinking about this the other day. My mom's godmother died when I was about 6, and I was really unemotional. I loved her, she was a really good family friend and I spent a lot of time with her... I just didn't really comprehend her passing. I suppose I was sad, but I guess being young you move on.. quickly? I felt quite guilty for not being upset, but I think it's a normal thing for some people.
The same with my dogs. I had 2 Maltese of the same who have been with me my whole life, and about a year and a half ago they both passed away within 2 weeks of each other. I cried a little when they first left, but otherwise I got through it quickly. Only now looking back do I realize how much I miss them, and cry about them and get upset. But it's okay to be emotional if you are eventually... it happens to everyone, and sometimes it helps to get it out.