He admitted his failure abjectly in front of everyone, almost begging for forgiveness.

abjectly 是形容词 abject 的副词形式。abject 由前缀 ab-（表示"离开、向下"）和词根 ject（"投掷"）组成，原意是"被抛弃的、卑贱的"。abjectly 表示"卑躬屈膝地、低声下气地"，形容一种极度谦卑甚至自我贬低的态度。