Oh I am so sorry to hear that, but try not to feel you made a big mistake, 13 y.o. is a pretty long life for the average dog, it also says that you were and still are a good "dog parent", such decisions like putting an animal down is never easy and it really breaks our hearts, but I have learned (though I am not fully convinced) not to have guilt, it is humane when an animal is suffering, and in many instances robs him or her of their dignity.
I wish I could give you some comfort but I know you are hurting, so best I can do is send you some hugs.
Whenever we have obtained an additional dog, it will never replace the first, etc. I have found that out, they are all individuals, like children, but a very warm thing is that we can love them regardless. I wish you love, and luck in becoming a "dog parent" again, somewhere out there is a dog who will be very lucky to have you

((((((((((((( hugs to you )))))))))))))

Sincerely,

DE