Take some time to read this thread at Testy Copy Editors on big mistakes. You'll read headline stories of people being killed prematurely, people being "assinated," alleged robbers being libeled. (The thread started last year, died off for a bit and has sprung back to life.)
What's nice is that in addition to sharing stories of other people's misfortunes, many editors own up to their own mistakes -- now, years later, that they can be at peace with them. I always like reading these stories because I know I'm not alone in screwing up.
My most recent error happened just last night. I was in charge of compiling the "people column," mixing in all the gossippy tidbits from all our wires. I was diligent about checking with other departments if I pulled something from their wire. "Are you taking Rosie's marriage?" No. "Who else has stuff on 'Passion'?" Everyone. "Are you using that Tyson piece?" It's all yours.
So I had checked the Mike Tyson item with two departments -- but not the most important one, sports. I got distracted right after I wrote down the number. And, of course, sports was using it. An alert co-worker found the repeat after the first edition. I made my apologies and quickly subbed out the item for the next edition.
Once I was done with the self-flagellation, it was time to see what I could learn from the experience and move on. Today's a new day (but one in which I won't screw up, let's hope).
It may not seem fair that we are held to higher standards than employees who makes countless errors every day. But I don't have a problem with that. If it is our job to erase errors, few things could be worse than our inserting them.
However, you're not going to be fired for one mistake. You may be fired for making a habit of them. So own your error and try to never repeat it. Explain how it happened, but never excuse it.
And then go back and read this thread; it might make you feel better.