This is how I read the song :
The narrator is a milkman, who used to deliver milk at the girl's house. They used to have a love affair, and drink milk together. Yet, one day, he finds the girl has left the house (either because she moved out or because she died --> possible interpretation due to the word "shrine" ???), so he is no longer drinking milk with her as he delivers the milk and the bottles are left unopened.
This is how I read the song : The narrator is a milkman, who used to deliver milk at the girl's house. They used to have a love affair, and drink milk together. Yet, one day, he finds the girl has left the house (either because she moved out or because she died --> possible interpretation due to the word "shrine" ???), so he is no longer drinking milk with her as he delivers the milk and the bottles are left unopened.