I was reading an article about shooting Chamois in Austria a few days ago that got me thinking. It commented that the norm in Austria is after the shot to wait until the rest of the herd has moved away completely out of sight before the hunters go up to the dead animal. The theory being that Chamois are never educated to the sound of a shot being associated with man.
Certainly I have noticed with both red and roe that other beasts just hang about and are not too concerned about the sound of a shot, but only run off once they see / smell you.
I tend to leave a beast for a few minutes before approaching, but letting everything else calm down does make sense to me as next time, hopefully they will be not too spooky!