Do you think that animals feel regret?
Yes, I do.
Back when my dog, Luna, was a puppy we would play quietly on my bed. It was a routine we did as I was waking up each morning or after a stressful day at college. We'd lay on our backs and I would tickle under her muzzle. She would attempt to "nibble" my fingertips and would swing her paws to try to trap my arm. I'd also blow lightly into her nose or lightly pinch her canine teeth. The play wasn't rough, but rather quiet, gentle, relaxing, and bonding.
When she was maybe 6 months old, we were doing this same thing one lazy Sunday afternoon. I don't know if she swung or I rose up into her paw... but she sliced my right eyelid open.
I make sure all my animals know some very basic commands as soon as possible: "No", "Stop", and "Come". When I ordered "stop," she stopped instantly and froze in place. I de-tangled her little nail from my eye and ran to the bathroom.
While I waited for help to arrive, I cuddled her. She was very distressed, cowering, submissive.
I ended up going to the ER to get stitches. It wasn't bad, there wasn't any damage done to my eye... it was just my eyelid. (I found out years later I do have a very small scratch on my cornea.) In fact, I was cracking jokes as I went through the ER and got my Tetanus booster, etc.
When I got home, though, my beautiful puppy was still cowering. Still far more submissive than normal. Every time she looked up at the bandage over my right eye, she was whimpering. Even after my eye healed, she'd see a bandaid and would become distressed.
Eventually, she became my service dog. But she still doesn't like seeing bandaids or wound dressing.