Answer by Rory Young:
Elephants are known to try to cover people or animals in branches after they have killed in rage.
They are one of the few animals believed to empathize. They also have a more developed hippocampus than we do and this organ is linked to emotion through the processing of certain types of memory. They are believed to suffer from flashbacks and Post Traumatic Stress Disorder. However, they also can, and do, kill..
The reason for killing is not of course to eat as they are herbivores, it is out of fear or rage, both of which are quite common amongst elephants. It is a survival mechanism.
Imagine then that an elephant has killed out of fear or rage and then settles down. It is inevitable that their natural empathy and their emotional memory will come into play.
Is this anything but regret? If not, then it is very close to it.