That should be posted in every office, every job site, every workplace ever. Seriously.
My own personal method has evolved through the years. When I was younger and stupider, I listened to the idiots who told me that “we” should never use language that cast the company in bad light. Never admit fault. I got older and smarter, and learned that people want basically two things when I/we screw up: they want an apology, and they want someone to fix things to the best of their ability. I learned that it’s lots easier and less fraught to go ahead and say “I’m sorry. We screwed up. Here are the steps I’m taking to fix this, here’s how we’re trying to ensure that you aren’t inconvenienced or financially burdened by our mistake, etc.”
I’ve had my share of professional triumphs, but the moment I’m most proud of? Our hotel had valet parking as the only option for parking on-site. (The garage was way too small and awkward to just trust the general public in.) One night, the cars were stacking up in the porte cochere and spilling out into the street, so the general manager decided to “help.” I got to the office the next morning, with a note on my desk explaining that Charlie had backed the brand-spanking-new sedan (seriously - it still had the drive-out tag) into a pillar. And the client didn’t yet know. Whee! I had a valet bring the car up and park it right outside my office, and let the front desk know to come get me the very second our guest came to check out. I met the lady at the desk - nice older woman from North Carolina, on vacation with her son and grandchildren in Savannah. I told her what happened, apologized profusely, walked her outside to show her the car, and offered her two options: she could spend another night in town, on our dime (free meals, room, and parking,) and we’d have the car repaired by the morning. (I shamelessly used my connections to get a good, local paint and body shop to agree to the job on a Sunday - I used to date the owner!) Or, “here’s the information for our insurance, your car is perfectly safe to drive, have your own shop send us the bill.” (And, of course, I comped the guest room and parking for her entire stay - IIRC, three nights, so about $450.) Before it was all over with, the nice lady from North Carolina made sure I had her phone number, and a standing invitation to stop in for supper any time I was in her neck of the woods, and we hugged and all that stuff. Because I owned up to the mistake on our part, and did everything within my power to fix that mistake.
The really funny bit was that the car was parked right outside the general manager’s window while this whole conversation was happening. He watched the entire exchange, and saw the whole hug/stop in for supper portion. When I got back into my office? Charlie came knocking, and told me “I don’t know what you did, but clearly, we aren’t paying you enough.” 