I am very sorry for your loss. The death of a parent is a significant life event. Dr. Elisabeth Kübler-Ross identified five distinct stages of grief that people experience when they are dealing with a loss or a tragedy. Dr. Kübler-Ross describes these stages in her 1969 book entitled On Death and Dying. Her model of grief was developed to help individuals cope with the death of a loved one. You may be experiencing depression, one of the five stages of grief.
Stage 1: Denial. During this stage, there is often a sense of shock and denial. People describe feeling emotionally numb. It is almost as if they don’t believe their loved one is gone. Denial is an unconscious defense mechanism. In this regard, it serves a protection function and it helps lessen the impact of the loss.
Stage 2: Rage and Anger. During this stage, an individual may wonder “why me? What did I do to deserve this loss?” It is not uncommon for individuals to become angry at the person they lost. They may think “why did you leave me?”
Stage 3: Bargaining: For many, this stage may include striking bargains in an effort to regain part of their loss. For instance, an individual may pray to God promising to do something good in exchange for a favor. “If I do this for you God, will you allow me to wake up from this horrible nightmare?” Even agnostics and atheists sometimes attempt bargaining with God during this stage.
Stage 4: Depression. This stage can bring about feelings of complete despair. At this stage, reality has set in. An individual begins to realize the enormity of their situation. Some people feel a deep sense of loss and think “how can I go on like this?” This is the stage I believe you may be currently experiencing.
Stage 5: Acceptance. By this stage, an individual can fully accept the reality of the situation. They are better able to cope with their loss. They are now in a position to work towards healthy alternatives to cope with their loss. For instance, an individual whose mother died of cancer may feel compelled to start a support or education group to help other family members who have lost a loved one to cancer.
Not everyone will go through all of these stages and some may get stuck in the earlier phases and never progress to the later stages. It is a idiosyncratic process that varies from person-to-person.
To answer your specific question, it is “normal” to feel the way you do. It becomes abnormal and considerably more worrisome if your intense feelings of despair linger or if they significantly interfere with your everyday life. In such a case, consider professional counseling. You could also benefit from a grief and loss support group.
I would also recommend reading about death and dying and other related topics. Many people who do so report feeling less grief associated with the loss of a loved one. They also report feeling more comfortable with life and death issues in general. Books that I would recommend include: Many Lives, Many Masters by Dr. Brian Weiss; Life After Life by Dr. Raymond Moody and The Wheel of Life: A Memoir of Living and Dying by Dr. Elisabeth Kübler-Ross. These books might assist you during this very difficult time in your life. Good luck and please take care.