He confessed having done a mistake.

Confessed : admit that one has committed a crime or done something wrong.
Granted : admittedly; it is true (used to introduce a factor which is opposed to the main line of argument but is not regarded as so strong as to invalidate it).
Conceded : admit or agree that something is true after first denying or resisting it.
Acknowledged : recognized as being good or important.
Concealed : kept secret; hidden.

Antonym of Confessed is Concealed