I put my dog to sleep and now I feel bad?

Yesterday morning I went to my mom's house. I was checking my dogs until I saw my dog Brownie looks very sad, so I told my mom that he didn't look good. So she told me that a week ago she caught him eating rat poison, so she thought she really didn't eat it, well he was looking very thin and very sick, so we took him to vet then he just say that he was not poison on dehydrated so they give him a vitims and fluids. When I went home I call my mom back later that day asking if the dog was okay. So the my dog was getting worst. I went back to my mom house there I saw my dog very sick he was breathing really fast and didn't want to eat. So we took him to another there the vet told us that he was in critical condition that we need to send him to the emergency vet hospital. As we took him the doctor told us that he look very sick and that he had blood in his lungs. And that he was bleeding internally so his condition was poor and that he need it blood transfusion and keep him the hospital but there was not survival changes to recover so me and mom made the decision to put him to sleep he was suffering. Now I feel really bad. How do I cope with this.