Just apologize a couple more times and offer to do whatever it takes to make it right and all will be forgotten.
Let me tell you a story of one of my biggest mistakes. I started at a company and the second week I was there, they wanted me to upgrade the help desk ticketing system (Remedy -- god that sucks!) and install it on a new server. I had no Remedy experience and thought "Sure, what the hell."
So I built the new server and was having issues with the configuration. So I pulled up the production server in one window and the new server in another window. I decided I had made a mistake in my SQL install on the new server and wanted to start over. So I uninstalled SQL....
Guess what? I uninstalled the PRODUCTION SQL server -- I selected the wrong window when I did the uninstall. It was my second or third week there and I almost broke down I was so upset. It took me a few days to get everything back up, but I got it all up and running and all was forgotten. When I left, I was the best employee in the department and they loved me and that wasn't even the only mistake I made.