I Keep Reliving It

I had to put my precious cat Libby down on Tues of this week. She had some sort of lung disease we fought for almost 2 yrs. She was comfortable until the end when her breathing got out of control and she was using her abdomen to help her breathe. I knew without a doubt I had done everything for her that I could and my vet confirmed this. However as prepared as I thought I was to hold my sweet girl and watch her drift away for the last time it did not go nearly the way I thought it would or had been told it would. Just about everyone I talk to says they pretty much just close their eyes and go to sleep for the final time. However, to my dismay my poor Libby fought...she tried to climb me and was gasping for air and gagging. It was the most horrible thing I have seen. I did feel at peace for her once all was quiet and her discomfort stopped. However I still feel so guilty and am making myself sick worrying that she was so scared in her last moments. I feel like I let her down. Did anyone else have an experience like this and/or is this normal? I need to stop reliving this and let her spirit rest in peace within me. Help!