He bowed his head contritely and admitted his mistake.

contritely 是形容词 contrite 的副词形式。contrite 来自拉丁语 contritus，意思是"懊悔的、悔悟的"，指因做错事而感到内疚和后悔的状态。contritely 表示"懊悔地、悔悟地"，描述一种带着悔意的态度或行为方式。