Calling or arriving 'at an ungodly hour' may suggest disregard for others' sleep or routines. Sorry for calling you at an ungodly hour, I forgot the time difference.
Pro Tip 2/3
Exaggerated Expression
The phrase is often used hyperbolically to describe times that are simply inconvenient. I have to leave at an ungodly hour to catch my flight at dawn.
Pro Tip 3/3
Informal Setting
It's mostly used in casual conversations rather than formal or academic situations. We stayed up chatting until an ungodly hour.