euthanasia and the sick chick

Hi Chicken lovers.....today I euthanized my first chicken. She has been sick a while and had lost weight and no longer would eat or drink. She had completely separated herself from the flock and was barely responsive to being handled. I used dry ice in an enclosed box. It took only a few minutes but I'm not sure it was the most humane way. Her name was Sage, and she was an Amerecauna....I think 3 1/2 years old. I did separate her from my flock when I realized how sick she was. Kinda lost right now....I work in the animal field, but it feels different when it's at home. How do you all get through the times that aren't so bright??