Ever since he got a new pet, he has looked very happy.
since 'looked' is an intransitive verb I would say that happy is an adverb explaining how he looked.
However on the dictionary happy is classified specifically as an adjective. (and happily as an adverb)
Am I incorrect to say that happy is an adverb on the above sentence.
not a teacher
'Happy' is an adjective. An adjective describes a noun (his look).
'Happily' is an adverb. It describes a verb, an action eg. lives happily.