Emily's reaction to the death of her father is one of denial and clinging to unrealistic expectations; it is also very telling of her state of mind and serves as a foreshadowing of what is to come with Homer.
The first thing we find out is that the only thing Emily is left with, upon the death of her father, is just the house. The family, whose members considered themselves to be "mightier" than the rest of the townsfolk, was apparently all about appearances. The finances must have failed, for Emily was left, essentially, destitute.
At last they could pity Miss Emily. Being left alone, and a pauper, she had become humanized. Now she too would know the old thrill and the old despair of a penny more or less.
That fact aside, notice what happens to Emily upon the death of her father.
Miss Emily met [the ladies offering condolences] at the door, dressed as usual and with no trace of grief on her face. She told them that her father was not dead.
Miss Emily lived with the body of her father inside her home for a number of days before she is forced to give it up for proper burial. At this point, she is in complete denial of his death. She is not dressed in mourning, she is not upset, and she even expresses these outlandish beliefs to others.
She did that for three days, with the ministers calling on her, and the doctors, trying to persuade her to let them dispose of the body. Just as they were about to resort to law and force, she broke down, and they buried her father quickly.
The use of the word "quickly" is one subject to interpretation. Why so fast? Was it because the body was already decomposing? If so, imagine the situation, years later, when it is Homer Barron's dead body that is left in the house to decompose for years until it turns almost into dust.
Is it because they feared that Emily would steal the body? If so, what kind of neighbors are the people of Jefferson to fear this sort of thing and not call a mental institution to go and get Emily?
Is it to hide the fact and let the people forget about it quicker? Probably so. Or it may have been mere practicality so that, once she calmed down again, the fight over the body might not be resumed. This incident reveals the small-town mentality that Faulkner embodies in the townsfolk narrator of this story.
Therefore, Emily's reaction is that she denies the death, keeps the body, and expects to continue living as usual until she is forced to snap out of her mindset and finally accept what has happened. This is indicative of Emily's extremely codependent personality, of her morbid inability to let go, and of her psychological inability to change and move forward.