na-adjective, noun
clumsiness; awkwardness; ineptitude
Refers to a lack of skill or poor handling of a task, often implying a mistake or failure due to incompetence. Used for both personal and organizational shortcomings.
彼の不手際で会議が混乱した。
The meeting was thrown into confusion due to his clumsiness.
このミスは私の不手際です
This mistake is due to my ineptitude.
下手 means unskillful or poor at something, often used for personal abilities. 不手際 is more formal and often refers to the handling of a specific task or situation.
Compound of 不 (fu, 'not') + 手際 (tegiwa, 'skill, handling'). The word 手際 originally referred to the way one handles things with one's hands, and the prefix 不 negates it, yielding 'lack of skill'.