noun
look of resignation; sense of resignation
Describes a facial expression or air that shows one has given up or accepted an undesirable outcome.
彼はあきらめ顔でため息をついた。
He sighed with a look of resignation.
結果を聞いて、彼女は諦め顔になった。
Upon hearing the result, her face took on a resigned expression.
諦め is the abstract noun 'resignation' or 'giving up', while 諦め顔 specifically refers to the facial expression showing that feeling.
Compound of 諦め (あきらめ, 'resignation', from verb 諦める) and 顔 (がお, 'face').