If the question is whether or not to backshift indirect quotes from deities, then the answer is that it depends on the context. To add on to JavaLatte's answer: As a related example, most (if not all) of the quotes from God in the Bible are direct rather than indirect quotes.
And God said, “Let there be light,” and there was light. (Genesis 1:3)
I imagine it would seem slightly disrespectful for the religious to indirectly quote God, as if they were reinterpreting the words. Which is to say, in actual scripture and other religious texts, use direct quotes.
Lord Shiva said, "I am responsible for everything."
In non-religious texts, such as scriptural analysis, opinion, and other related essays, it depends on the intended audience. If the audience is religious, again, I suspect it's a good idea to use direct quotes as much as possible to show that you are not changing the words in any way.
For non-religious audiences, it doesn't matter. Since you are talking about a figurative entity, you can treat Shiva the same as a classical scholar would talk about any of the ancient Greek gods, using backshifted indirect quotes:
To Paris was given to judge who was most fair and would win the golden apple. First Hera, Queen of the Gods, stood forward and offered to make him a mighty king, ruler over many lands. Then Athena, Goddess of Wisdom spoke, and offered Paris the gift of wisdom, that he would be so revered among men that many would come from far and away to seek his counsel. Lastly, Aphrodite, the Goddess of Love, offered him the most beautiful woman in the world to be his wife.