Hello Fan: Welcome to PsychCentral!

I'm sorry you had this disturbing experience.

From what you wrote, it seems to me the fault here lies with the shelter & their lack of flexibility. I see absolutely no reason why you should not have been given the option of coming back for the kitten if the shelter determined they could not care for it.
I hope that, with time, you will be able to let your grief & guilt regarding this go. I know how this sort of thing can eat at you.

Here are links to 4 articles, from PsychCentral's archives, that talk about grieving the loss of a pet. Of course this kitten was not really your pet. But hopefully some of the insights in these articles will be of some help in coming to terms with this:
https://psychcentral.com/lib/grievin...loss-of-a-pet/
https://blogs.psychcentral.com/live-...a-pet-is-real/
https://psychcentral.com/lib/the-15-...et-loss/?all=1
https://psychcentral.com/ask-the-the...death-of-pets/
My best wishes to you...