For instance, your invocation of "introspection" is covered in the linked article by "theory of mind". And maybe in the second paragraph covering metacognition in "consciousness". I think this quote covers the ideas succinctly:
"Convergent evidence indicates that non-human animals have the neuroanatomical, neurochemical, and neurophysiological substrates of conscious states along with the capacity to exhibit intentional behaviors. Consequently, the weight of evidence indicates that humans are not unique in possessing the neurological substrates that generate consciousness. Non-human animals, including all mammals and birds, and many other creatures, including octopuses, also possess these neurological substrates." [0]
We've found evidence in some animal or another for pretty much everything we've ever thought was unique about human cognitive abilities. So far, the only unique thing about humans is how broad and powerful our cognition is. Which is maybe what you mean, and are having a hard time expressing.
[0] http://fcmconference.org/img/CambridgeDeclarationOnConscious...