I have had a similar experience as you, ACSAPA, which I will mention in a minute. So, I understand the emotions you experienced.
I think there is a difference between seeing an animal die and finding a dead animal. I've seen my share of squirrels, opossum, and birds that have died, usually hit by cars. There was one Spring where three baby birds died in my yard. They must have fallen out of the nest. It was sad to come upon them. But, I think we come to expect things like this.
Seeing an animal get hit by a car is a completely different experience. It is one that psychologically affects me for a long time.
I have had the experience of having a beloved pet die in my arms. Three years ago, my Lab who was almost 14 became very ill one afternoon. She woke up fine, had breakfast, went about her normal routine. Then, about 2 in the afternoon she didn't look well.
Two hours later she was throwing up repeatedly. I tended to her sensing that something was different this time. Within the hour, she died as I was trying to keep her comfortable. It was numbing and heart wrenching at the same time. I've never had a human died in front of me, but I suspect it is as surreal. Someone who was once alive is no longer and it happens before your eyes. You don't shake that easily.
I must say that it was a relief and a comfort to know that she had died on her own terms at home. She made it easy for me. I did not have to make that decision of when to put her to sleep. Though, I don't think I want to repeat the experience any time soon.