Animals are tough and fragile at the same time. From my point of view, you did everything right and the loss isn't your fault. I know it's really hard when you get into that mothering state and the creature dies anyway, but... it's probably for the best.
Over here, we have pretty much unlimited resources. My husband is a veterinarian, he does large and small animals and has a mobile vet truck so he not only has knowledge and skill, but also equipment right here. HOWEVER, we would have done the same thing as you. Clean it up, keep it warm and wait and see.
Just because you CAN doesn't mean you SHOULD. If we are reactive and intervene too much, we would eventually end up with weak stock. If we intervene less, nature assists us in culling leaving us with hardy stock. I have a really soft spot for management mistakes. If I screw something up and an animal is injured I'm going to insist we intervene.
The only thing I can think of that you might be able to adjust for if there's a next time is learning better restraint for a chicken/chick. Chickens *cannot breathe* if their bodies are constricted. The only thing I can imagine you could have possibly done "wrong" is to hold the chick too tightly while you were trying to get the would cleaned up.
I recommend NOT getting suture supplies and antibiotic ointment. It's almost always best to leave wounds open to breathe and heal. Sutures can make a situation much, much worse. I can relate to the feeling that you haven't done enough, but you did everything you could, everything you should.
