It happens to everyone sooner or later. If you feel bad it just shows you have some compassion for the animal you are after. The feeling never goes away as it shouldn’t but you just have to go back out and try again, just learn from you mistakes.
I had it happen to me a few years ago in some National Forest here in MS. I shot the bird at 30yds and rolled him, when I was about to stand up he got to his feet and flew over me. I missed him twice as he flew by me. He left a pile of feathers and a blood trail most deer hunters would dream of. I trailed him until the blood stopped hitting the ground because of the pine trees. I looked for 2 hours then hiked out the mile to my truck and then went home 25miles to get my lab. I went back and wound up running into a Park ranger who was more than impressed I was putting forth so much effort in finding a bird. I told him I was sick that I didn’t make a clean shot and owed it to the bird to find him if it was possible. Me and my lab looked for another couple hours with no luck, the pines messed up the blood trail. I think of that bird every season, still don’t know what happened and prob never will.
What I did do is I put a Bushnell Trophy red dot scope on my gun and I use the Circle with the dot in the middle for my sight. With the choke I have the outside circle is the size of my pattern. If the turkeys head is inside of the outer circle I have 110% confidence in the shot. I also shoot NITRO shells yes they are $6 a shot but was that bird you just shot and lost worth $6. Yes you can still miss or mess up a bird with them if you make a bad shot but it puts the odds a lot more in your favor. The new Hevi-Shot magblend is nice also and less per shell.
Main thing is don’t beat yourself up over this to bad, just get back out there and find another bird.