Owning your mistake out loud ends the story faster than defending it ever will.

A defence keeps a mistake alive, because now there are two things to discuss: what happened, and whether you will admit it. People lose interest in the first one quickly. They do not lose interest in the second. Saying plainly that you got it wrong removes the only part that was still worth talking about, and the whole thing goes quiet much faster than you expect.

If there is something you have been managing rather than admitting, say it in one sentence to the person it affected. No reasons attached, no list of what else was going on. Then go straight to what you are doing about it.