have egg on one's face这个字面意思是“有个蛋在某人脸上”，是不是想到电影里面常有的情景，有人被群众扔鸡蛋，很狼狈的样子，所以引申为“丢脸；狼狈不堪”的意思。

【例句】

Everyone passed the exam but me,I had egg on my face.

除我之外，每个人都通过了考试，我丢脸了。
 

They were left with egg on their faceswhen only ten people showed up.

只有十人到场，他们感到很丢面子。