Kim,
Huggggs.
I know how hard it is to lose a special feline family member and also the particular pain and guilt to be at fault. For me, it was a little kitten born with horribly deformed back legs. My vet took a look at them and we chose, together, to put the kitten to sleep because the deformity looked so severe.
I now know that this form of birth abnormality is actually not uncommon in kittens and that no matter how deformed they may look, when given a towel in the nesting box to push against, they almost always grow out of the problem and the legs straighten out.
But neither my vet nor myself knew about this at the time. I still mourn the loss of that little kitten that wasn't given a chance to live.
So be comforted that you are not alone and that by sharing your experience you can help other kittens avoid the unfortunately accident that your little Emma experienced.