No. Not at all. She was doubtless just registering very temporary surprise is all. Over in a second. You chose to beat yourself up about it. Completely understandable. But not betrayal. Betrayal is when you keep her alive for the pleasure of having her by your side regardless of how it affects her. Real love is taking a decision for her which rips your guts out. That takes courage.
Art, what Maggie says is absolutely on the money.
I've had to take two dogs to the vet on their 'last journey' with me. By nature I'm a bit of a loner, and place great emphasis on my 'animal partner'. My wife often jokes I put the dog before her and my children. I don't, but I understand why she would say it. I spend all my waking hours with the dogs.
But I wouldn't hesitate to euthanize should I think for one minute that by keeping them with me caused any pain or suffering, even if medicines mitigated the pain somewhat.
My last dog developed a tumour on her spleen that burst. We had the choice to operate, or euthanize, the vet said we'd get at best 6 months longer if the op was a success, but he only gave her a 25% chance of coming through the op. I made what I thought was the right decision at the time, asked him if he thought she'd last the night at home for me to bring her back in the morning to be put to sleep. He gave us pain relief and a bag of fluids for my wife to administer if she became really poorly.
I took her home, we had the rest of the day spoiling her, she slept on our bed at night and had a huge steak for breakfast.
Myself and my wife then took her to the vet and said our goodbyes as she was put to sleep, and yes, I was convinced that I saw her look at me pleadingly, but I'll also tell you that we look for things like that, we want to beat ourselves up, and try to justify why/how we could have avoided doing what we did, it's in our nature as animal lovers.
If you honestly believe that what you did was best for your cat then you have nothing to feel upset/ashamed about. That pleading look you got could well have been one of relief, and understanding mate.
You were strong pal, if you were weak you'd have brought the cat home, and you know yourself it would have been born more out of selfishness on your part than anything else.