Everyone deals with grief differently, and each situation is unique to itself. If your pet is ill for a long time, and you have to choose to euthanize or not, you may not be mourning quite as long as someone who's pet was killed suddenly and unexpectedly.
It is important that no matter how your pet died, or how long you had them, that you acknowledge your feelings. If you act as though nothing is wrong, you are pushing the feelings to the side, and will end up having a harder time working through the grief. If, instead, you talk about your pet loss, you will be able to find your way to the end of the grief that much faster.
One way is to find other people who have dealt with situations like you have. Finding someone who has recently lost their pet in a similar way that you have is a good way to work through the despair. You can share memories and can help to realize that you should not feel guilty about their death, no matter if it was accidental or chosen. Pet-loss-memorial.com is one place where you can connect with others. You can leave stories about your pet so that other people can read and smile. Who knows? You might find yourself helping someone else get over the loss of their pet.