How did they justify belief in their gods? Same question for the Mayans (whose religious texts seem more widely available, so maybe more people would know).
There seems to be disagreement on even what they thought; most texts seem to agree that they believed enough in their gods and their myths in enough of a literal sense to justify sacrifice to continue the sun's cycle. Others suggest that they (I'll see if I can get a source for where I read this) mainly follow the idea of teotl, and that their gods are merely the incarnation of teotl, and are somewhat abstract. I've been trying to research this but there seems to be little information on the subject, and I can't figure out how they legitimize their claims, if they do at all.
I can't say I understand your question. Why does anyone believe in their respective god(s)? Religion isn't something you really "justify" to anyone.