I dunno OP. Id say you are fine. Killing something does suck. I had to kill a small hare a few years ago at college. The property I lived on had a couple stray cats on it that we would feed. One day I saw them playing with a hare...and taking turns pouncing it, backing off, pouncing agin...well you get the picture. They were playing with their prey.
I scurried the cats away so the hare could escape, but it wouldnt hop. I inspected its body and it had deep nasty wounds in its hind legs. No way it would survive in the wild without being eaten first by a predator, or dying of starvation from not being able to hop around to find food.
I called my good buddy and he told me the wounds were bad and that it would likely be put down if I took it to a animal hospital or shelter. So at first I grabbed a knife to put it out of its misery, but I couldnt bring myself to do it that way. My buddy told me what he does at his job when they find small injured animals on the runway.
Put them in a bag, leave it unsealed a little so they dont suffocate, and then as hard as you can, slam the bag on the ground. Itll knock the animal out cold, and then to do it a few more times for good measure. Afterwards seal the bag so it does suffocate just in case its alive, but it will die while unconscious. That was the best way for me to do it...because I wouldnt be able to handle breaking its neck, or slitting its throat to kill it. I wanted to do it in a way that would limit its suffering and limit the emotional toll on myself.
I felt like crap for a couple weeks (since I have small pets), but I didnt cry. It is what it is OP. Some people just cant handle killing things. I dont think its a big deal that your gf saw you cry over that. Compassion and respect for life is admirable.