Hero Is Gone And I Am Devastated

Two days ago I had to put my cat, Hero, to sleep. Even though I knew his time with me was ending I still couldn't believe it would be so soon. His kidneys failed and after a week of desperately trying to get him hydrated again, the vets said there was nothing more that could be done. I know that euthanizing him was the most humane thing to do, but I feel like I murdered him. My best friend was with me at the vet and we both started crying when the vet said that putting him back on the IV would only prolong the inevitable. The vet left us alone in the room together to decide if I wanted to put Hero to sleep and both of us knew it had to be done. The worst part was that when I brought him to the vet I really thought they would be able to help him, and when I think of how he meowed so pitifully when I lifted him from the bed into the cat carrier, my heart breaks because I took him from his home to his death. Also because of his illness we had to give him injections and stuff pills down his mouth, which he hated. As I was sitting there in the exam room thinking that if I had known it was his last day alive I wouldn't have put him through all of that, he got up off the counter and sat down in my lap. Even though I had put him through all that pain with the needles and pills, and took him from his home to a strange, cold place, he still loved me and trusted me. I put him back on the counter and my friend and I stroked him and told him it would be ok while the vet gave him the injection. He went limp barely a second later and I am still haunted by his open eyes as the vet took his body away. I keep playing his death over and over in my mind and I hate myself for being the perpetrator. While most people in my life have been very kind and understanding, I still feel cut off and alone, even from my best friend who also loved Hero very much. I know that putting him to sleep was supposed to be an act of compassion that would spare him further suffering, but I can't stop myself from thinking that he wanted to live. Everyone tells me that I did the right thing, but nothing consoles me. I feel an overwhelming ache in my chest and I can't stop crying. Any thoughts/comments would be greatly appreciated.