We have experienced this awfulness before.
It is awful because in a sense you (we, whoever) did in fact choose to have the pet put to sleep. Some inner ones would never make that choice (in me). And they were appalled and horrified that we did make it.
It was hard for them to accept the choice was made with a good heart, with the best intentions, or out of love. It was made with so much love and so much sadness. Those little ones could never understand that in us. How could a choice to have a beloved put to sleep be made out of love? How could it possibly be loving?? But it was. It the best bad choice. Choices had to be made and it was the best one available when none of them were good.

I know this probably hasn't helped you any. But you are right, it was best and right. Those poor littles. Look after them.