Every person deserves some sort of funeral service no matter how brief or inexpensive. A person has lived a life with some friends and family and their life should be acknowledged in some manner. It is certainly difficult to organize and participate in a funeral after the death of a loved one. Talking with many friends and relatives can be exhausting and emotionally difficult. However, it is an important part of the grieving process. It allows everyone to express their feelings and provide emotional support to each other. It is also important simply to say goodbye to your loved one. If you avoid having a funeral or memorial service, you will just prolong the grieving process. If your concern is about the expense of a funeral, there are ways to have an inexpensive service. Remember that the funeral is for the benefit of the family and friends not for the deceased. Even if the deceased had stated they did not want you to have a funeral, you should still have one for the reasons stated here. Please also realize that the deceased had other family and friends that are also grieving. You should reconsider your decision to not have a funeral in consideration of the feelings and needs of others. If you have some reasons for not having a funeral, I strongly advise you to overcome all your objections and issues and plan a short, simple and inexpensive memorial service.
My webpage on funerals has suggestions and ideas on how to plan for a funeral and do so at a low cost. See /practice-areas/funerals-burial/#arranging-for-funeral