I just had an experience that vividly illustrates this point. My wife and I went out for dinner at a local restaurant to enjoy a relaxing evening following a busy week. Our server was a bit hurried and seemed intent on hurrying us, since the restaurant was fairly busy, but that didn't pose a particular problem. It was when the dinner arrived that the experience deteriorated. It started with the server's simple mistake of not bringing a roasted vegetable side-dish that was supposed to come with my dinner; it was not a big deal to me, until the server made it one.
When I mentioned the missing vegetables, the server looked surprised and then disappeared. She returned after several minutes, tapped on my shoulder, and announced rather proudly that I must have made a mistake in ordering. Her response caught me off-guard, since I just figured that the missing veggies would be delivered and that would be the end of it. I asked for the menu to verify my selection; at that point, the missing side dish was presented while the server repeated her claim of being "right". At that point I felt compelled to ask for the manager.
The manager informed me that the server was new and the menu could be confusing; the first reason was beside the point and the second rather puzzling, since after all it was their menu. He glossed over the mishandling, said something about needing better training for his new servers, and then left our table. I sat there mystified at how a missing side dish of roasted vegetables had escalated to become a problem that was worth trying to justify. I wasn't concerned about the oversight, but I was unhappy with how poorly it was handled.
When something goes wrong, make it right. Don't spend time trying to justify your position and prove that you're right; attempting to explain away mistakes only makes you look bad and leaves the customer unhappy, no matter what you ultimately do or say.
If you take care of a minor problem swiftly, it fades away and the relationship remains intact. In some cases, a fast and fair resolution actually builds trust. If you choose to argue over it, however, you can count on damaging the relationship. It doesn't take much to make the damage permanent and to potentially lose a customer.
It's up to you to decide what happens the next time a mistake occurs. Will you let a minor problem linger or potentially make it even worse by trying to explain it away? Or will you just make it right?