He felt he would lose face if he admitted he didn't know the answer in front of his team.

lose 是动词，意思是"失去、丢失"。 face 在这里不是指"脸"，而是指"面子、尊严"。 lose face 是一个固定短语，意思是"丢脸、失去尊严"，指在公开场合出丑或丧失威信。