Bismillahir Rahmaanir Raheem
"Every month is a stage in a man's life. As a month ends and the new moon is signalling the beginning of the next month, it seems to announce that a stage in every man's life has passed and a new one beginning. The most suitable supplication at this time can only be: "O Allah! Cause the new stage, which is the new month, to pass with peace, security, faith and Islam, and make us obedient to You."
Because there are people in the world who worship the moon, Rasulullah (Sallallaahu 'alayhi wasallam) made part of the supplication as a declaration that the moon is merely a creation of Allah Ta'ala and just as Allah Ta'ala is our Lord so too is He the Lord of the moon."
[Commentary from Ma'ariful Hadeeth - Meaning and Message of the Traditions by Maulana Muhammad Manzoor No'mani (Rahmatullahi 'alayh)]