조상님 뵐 면목이 없다

면목이 없습니다. 

I'm deeply ashamed (of myself).

면목 means face and eyes, and it refers to face.

면목이 없습니다. "I don't have "면목 (面目)" means

I know my faults and others know them too,

so I don't have 면목 (面目) to meet others.

However,

"조상님 뵐 면목이 없다" means

feeling guilty or sad because I can't meet my ancestors.

It is used when you can't attend an ancestral rite or neglect the care of your ancestors' graves.

On the other hand, in the Confucian way of thinking, it means that you are embarrassed to meet your ancestors because you did your job poorly,

and it is also used when you cause a big accident or cause a social problem.