I'd suggest, other than the fact she needs to learn about 'drop'/'leave', this is quite natural. She's now resource guarding - is all. How can she possibly be sad when she's done what she's hard-wired to do. Chase, catch, kill - and most likely eat. If you don't want her eating wild animals, keep her better confined - and be aware that wild animals often carry tapeworm so if she does eat it, she'll need to be checked for this, eventually. She does need to learn to leave, in case she gets hold of something dangerous.