Almost nobody remembers the specific error a year later. What they remember is whether you owned it fast or made them dig for the truth.
There are two instincts that both make a mistake worse than it needs to be: hiding it and hoping it goes unnoticed, or over-apologizing to the point that the conversation becomes about managing your own guilt instead of fixing the actual problem. Both waste time. Both erode trust in a different way. The version that actually works is faster and less dramatic than either.
Say what happened, plainly, as soon as you know. Not after you've built the perfect explanation, not after you've quietly tried to fix it yourself first, as soon as you have the basic facts. The instinct to wait until you have a full solution before saying anything usually just shrinks the window everyone has to actually help.
"I made a mistake, I sent the client the wrong pricing sheet this morning, with numbers from last quarter's proposal. I've already sent a correction and a short note explaining the error. Wanted you to know before it comes up from their side."
Notice what's absent from that message: a paragraph of self-flagellation, an explanation of everything that was going on that led to the mistake, or a defensive justification. Just the fact, the fix already in motion, and a heads-up. That's a complete report. Anything longer starts working against you, because it shifts focus from the fix to your feelings about having made the mistake.
One apology is enough. Say it once, mean it, and move to what happens next. Repeating "I'm so sorry" multiple times in the same conversation doesn't make the apology land better, it usually makes the other person start managing your emotional state instead of focusing on the actual fix, which is an unfair position to put them in.
The part people skip that actually matters most long-term: naming what you'll do differently, specifically, not just generally. "I'll double-check pricing sheets against the current quarter before sending" is a real change. "I'll be more careful" isn't, it's a feeling, not a process, and it won't survive the next busy week. The specific version is also what turns a mistake into something that quietly builds trust instead of eroding it, because it shows the mistake actually taught you something concrete.