I know how you feel. I had a Calico cat for ten years that ended up with cancer. I had no choice but to put him down. My Wife drove us to the clinic while I held him in my arms and hugged him the whole way there. I told him just how grateful I was to have had him as a pet and what he had meant to me and my family.
When we got to the clinic, I hugged him one more time, told him I loved him and gave him to my Wife to take inside.
It was one of the hardest things I’ve ever had to do, so I know what you are going through. You did the right and humane thing.
She asked if I wanted to be in the room while they put 101 down.
They brought in a blanket and 101 laid down, me right next to him.
I talked with him the whole time, the sedative made him sleepy and he just put his head on my knee.
After it was over the vet told me I could remain in the room as long as I needed.
Several days later I got a sympathy card from the vet and the staff.