Own the mistake before somebody else has to point at it. It stings less and fixes faster.

Being caught and confessing produce the same facts and completely different reactions. Announcing it yourself keeps the situation about the error. Waiting until somebody finds it makes the situation about the hiding, which is always the bigger problem, and you lose the chance to be the person describing what happened rather than the one being described.

If something is wrong right now and you know it, say so today. Lead with the fact, then what you are doing about it, and skip the part about why it was not really your fault.