Loosing a pet is hard, I don't think there is a 'way of dealing' so to speak. I lost my old dog 2 years ago, from healthy happy senior dog to suddenly collapsing in the garden. Half an hour later he'd been put to sleep, massive internal bleed. We then adopted another dog, lost him 6 months later to acute kidney failure. It was heart breaking. I cried, I shouted at my husband even though he was upset too, I drove like a maniac all the way home from the emergency vets because I hadn't come back home with my boy. I was so angry, so very angry. You just deal with it the way you have to. If you have to cry, then cry, because it's what you need to do. I'm so sorry for your loss
I'm so sorry. Your reaction is normal. Of course you are going to cry, it is because you loved your cat and now they are not physically with you. Take your time and be kind to yourself. I felt utterly bereft when my old mare died, I didn't think I would ever stop crying. I am still tearful about Toffee and Ripple (guinea pigs) who died before Christmas. I feel their absence and miss them every day. Time does not exactly heal, but it does allow the emotions to be dulled a little, and then you are able to remember them with joy, instead of sadness.
I am very sorry! Grieving is the other side of the coin called love. We are free to love our pets in a way that we often can't in other relationships, and the love they give us back is as unconditional, too. So when a beloved one dies, it hits you really hard. Your reaction is not all unusual. Unfortunately, you have to grieve as much as you have loved; there are no shortcuts - but without the love and joy, your life would have been so much poorer! Give yourself time and space to grieve; it doesn't matter what species - the crucial bit is what kind of bond you have had.
If you find that you keep on struggling with sleeping and/or coping with your daily life for any length of time as a consequence, please contact one of the free addresses listed in this link to get somebody with specific training to listen to you. Pet bereavement is recognised as a serious issue that can hit anybody, so there is no shame in getting knowledgeable help: http://www.supportline.org.uk/problems/bereavement_pets.php