I doubt you could teach animals 'moral concepts.' First of all, the animals would need to understand our language. Second: They need the ability to understand ABSTRACT ideas. Morality is not something tangible. It is a set of ideas (of 'right' and 'wrong').
I have never heard of an animal that can understand our language and can be taught 'abstract' ideas.
It would probably be impossible to teach animals morals. But then again, you don't see bees performing their 'bee dance' (that indicates where flowers with nectar can be found) for ant eaters. Ant eaters don't understand and don't care about nectar, and animals don't understand and don't care about morals.
You are correct if you say that 'morals' are purely a human thing. Saying that it makes you better than any other animal is not based on any information though.