People are human, and as such, we make mistakes. There is not a person on earth who has not made one. The key is how you handle -- or respond -- to the matter.
My husband and I were out shopping one day, on the hunt for dress slacks for our son in honor of a special occasion. We found exactly what we were looking for -- and they were on sale, 30% off, according to the sign. Yup, we were happy!
However, when the sales clerk rang them up, the regular full price was shown on the computer. We pointed out the discrepancy to her and, without saying a word, she walked off to check the signage. A few minutes later, she returned to the register, re-rang our pants, asked for my payment and that was the end of the transaction.
What happened to the idea of acknowledging an error? We weren't looking for an apology, but a little conversation would have been nice: "You are correct, they are on sale"; or "That's a great price for these slacks!"; or even "Well, it seems like the computer is off, let me make that change for you". Instead, we got silence ... and you know there was no "Thank you for your purchase / coming in today."
People don't like to be wrong but it doesn't have to be a big deal. Take responsibility for the problem, even if you did not cause the error. Address the issue and then move on.
You can apologize. "Gosh, I'm sorry this happened. Let's see what we can do to fix it." ... and move forward. This is a matter of simply showing empathy for the situation.
You can thank the person. "Thank you for bringing this to my/our attention. Now that we know about it, we can correct the mistake." This is an action statement; the apology is implied.
There are a number of ways in which a mistake can be handled; the first thing to do is acknowledge it.