Dear Sleepless: Oy. You don’t say how long ago this happened, but you need to quit putting off what is undoubtedly going to be a very difficult chat—not just for you, but for your boss, too. “Don’t let any more time pass without speaking to him about this,” says David Maxfield, vice president of research at training and consulting firm VitalSmarts and co-author (with Joseph Grenny) of a book called Crucial Conversations. “Silence is an admission of guilt, so procrastinating will just make things worse.”

To have any hope of redeeming yourself, you’re going to have to fall on your sword. “We tell our executive coaching clients in this kind of situation that the bandage has to be as big as the injury,” Maxfield says. “And this is a very big injury, with two parts. First is what you said, and second is the fact that the boss wasn’t supposed to hear it. Your apology needs to cover both.”

So, first, admit to him that you shouldn’t have said what you said. “You really have to come right out and say, ‘I screwed up, and I’m sorry.’ Acknowledge that your comments were inappropriate, and that you weren’t your best self at that moment,” Maxfield advises. To be effective, he adds, “an apology has to show some element of sacrifice, even if it’s only your ego that suffers.” One executive he knows who committed a blunder similar to yours when she thought her phone was set on “mute” (alas, it wasn’t) sacrificed time and money as well, by “flying clear across the country on her own dime so she could apologize in person.”

Second, it’s important to address the fact that you were talking behind his back. “Especially since he’s a relatively new boss, who probably already has concerns about being accepted, you need to make it clear that you weren’t trying to gang up on him by ‘recruiting’ coworkers to your point of view,” says Maxfield.

Beyond that, since your rant was apparently critical of certain decisions your boss had made, you’d be wise to mention that too. “Never lie to your boss by pretending you don’t think what you really think,” says Maxfield. “You can’t paper over disagreements.” This is tricky, but you could, for example, bring up a specific criticism from your ill-fated monologue. Say that you regret not having talked about it with him privately to get a clearer idea of the thinking behind the changes he’s made, instead of spouting off to all and sundry in the hallway.

The hardest thing to recover from, according to Maxfield, is having said your boss is unqualified for his job. The plain fact is, he may never forgive you for that (even, or perhaps especially, if it’s true). “It would be nice if you made an abject apology and all was instantly forgiven, but that only happens in Disney movies. It’s not real life,” Maxfield notes. “All your apology may really do is introduce an element of doubt. Instead of being sure he can’t trust you, he may be willing to wait and see.”

By the way, although it probably won’t make you feel any better, VitalSmarts recently surveyed 775 U.S. employees and found that 69% admitted they had said something at work that they later had cause to wish they hadn’t. Of those, VitalSmarts reports, 27% said inserting foot in mouth had “undercut or destroyed a working relationship,” and almost one in three (31%) said it “cost [them] a pay increase, a promotion, or their job.”

To avoid being in that latter group, Maxfield says, you will have to “prove your loyalty going forward. Invest extra time and energy in your work, and see what happens. As time goes on, are you getting good assignments? What about raises?” Be patient. If, despite extra effort, you’re still persona non grata with this boss after six months or a year, he adds, “it will be time to seriously look for another job. Or, if you don’t want to wait that long, start now.”

Good luck.

Talkback: Have you ever said something at work that damaged your career? How did you recover from it (if you did)? Leave a comment below.