This is the most difficult sentence for companies that stumble in doing effective customer service.
By effective, I mean customer service that pays for itself, that is a rational expense on the way to building a loyal brand following and generating positive word of mouth.
When someone in your organization says, "You're right, we were wrong," they're not saying that you're always wrong, or that you were completely wrong, or even that, in a court of law with a sympathetic jury, you would lose. It certainly doesn't mean you didn't try.
No, all you're saying is that you made a promise or set an expectation and then failed to live up to it.
Owning that and saying it out loud does two things: it respects the customer and it allows you to make more promises in the future.
If it helps, you can remind yourself that this is investment in your ability to make a promise tomorrow.