apologetic
adj.adj. feeling or showing that you are sorry for something you did. You use this to describe a person's face or a person's way of speaking when they are in trouble.
adj. expressing or showing a feeling of regret or guilt. Often used to describe a person's facial expression or manner of speech when they are apologizing.
He gave me an apologetic smile after he broke my favorite pen.
The manager made an apologetic remark about the long wait, though the customers were already leaving.
Her apologetic tone suggested she felt responsible for the mistake, even though the error had been caused by a system failure beyond her control.
From French apologétique, from Latin apologēticus, from Ancient Greek ἀπολογητικός (apologētikós, “of or suitable for defense”), from ἀπολογέομαι (apologéomai, “to speak in defense of”); see more at English apology.