For many, acceptance means agreeing to reality. Most of us, when we lose someone dear to us, simply don't want to agree to it; we actually have an aversion to agreeing and accepting. So, let's use a different word—try "adjustment", or "integration". Both words focus on the purposeful release of disbelief. Someone who has integrated the death of a loved one into their life has cleared the path to creating a new life; a pro-active life where a loved one's memory is held dear, perhaps as a motivating force for change.
It does take time. In "Coping with the Loss of a Loved One", the American Cancer Society cautions readers that "acceptance does not happen overnight. It’s common for it to take a year or longer to resolve the emotional and life changes that come with the death of a loved one. The pain may become less intense, but it’s normal to feel emotionally involved with the deceased for many years after their death. In time, the person should be able to reclaim the emotional energy that was invested in the relationship with the deceased, and use it in other relationships."
Whatever you call it, this essential part of mourning is what allows us to live fully again. It allows us to step out of the darkness of mere existence and back into the sunshine where life is sweet again. Of course, it's a very different life than the one you had before your loved one died.