How can I get over the grief!?

So my cat died about a week ago. We had him for nearly 10 years and didn't think it would affect me so much but it is just starting to hit me how much I miss his fuzzy little face. I found old photos on my laptop of him and it has just set me off crying. I don't really know if other people get like this over the death of a pet but I really can't help myself right now. Its weird that he is just... gone. Is it normal to be this emotional over a cat and how can I "get over it" as such. I guess I feel guilty because I knew he seemed a bit ill a few days before but didn't think much of it. I think it is the guilt that is most getting to me. :'(