The answer is that the funeral can look backwards—and forwards.
The alternative to a mainstream religious funeral is a reflective ceremony which looks back over the life lived and records and celebrates everything about that person which has not been lost: their memory, their values and their example, all of which live on. If non-religious people are to derive any comfort from a funeral it must be in the consideration of how they can look forward their own lives continuing to be enriched by the person who has died. Much as they miss them, they would far rather they had been a part of their lives than not. This is a good pain they are feeling.
A ceremony like this can do exactly what people want a funeral to do: focus on the life of the person who has died and give thanks for that life. It can incorporate that person’s wishes, beliefs and values, and those of their family and close friends, so it is much more personal than a religious ceremony, which puts god first and which has a fixed format to which you can contribute very little.
Better still, you, the organiser, have complete control over what happens.
But remember: happy memories and fond feelings do not themselves necessarily help us to make sense of death. They may serve to remind us only of how sharply we miss the person who has died. People who have not adopted or evolved a belief system which explains death have to make sense of it their own way. That is their responsibility, not yours.