In my language, we have a phrase which roughly translates to "don't roll around where you've fallen". It indicates that a person has said or done something stupid. Then when someone points this out, they still don't stop and pretend to be right, in order to avoid shame due to being wrong. Hence the phrase means: "You've already fallen, don't try to roll around and pretend you're still up".
When you're in a hole, stop digging.
Michael Josephson has this to say:
Most of us have lied to get out of trouble. From childhood denials (“It wasn’t me!”) to adult fabrications (“The check is in the mail…”), what seem like harmless falsehoods easily fall from our tongues. And then we make up more excuses or tell more lies to protect the first one. Soon the “cover-up” is more serious and credibility-damaging than whatever we lied about in the first place.
The natural tendency to avoid discomfort makes our lives more difficult in other ways as well. Some people damage or endanger their most important relationships at home or work by failing to acknowledge and deal with small problems that then fester into serious ones.
Here’s a useful piece of advice: “When you’re in a hole, stop digging.” Whether our problems are of our own making or not, whether we know exactly how to resolve them or not, the first step is to stop making things worse. Stop making excuses. Stop blaming others. Stop ignoring our strong and persistent feelings. And stop dismissing and discounting what others are telling us about their needs and feelings.
Once we stop digging, we can work on getting out of the hole. It may take more honest self-reflection, self-restraint or simple will power. Perhaps we have to adjust our schedules or simply be more attentive and considerate. Sometimes the best thing to do is ask for help and someone will throw us a rope.
Like so many aspects of character, this is often easier said than done. But when we manage our lives thoughtfully and with integrity, things do get better.
It is often associated with the British politician Denis Healey (reference to the Telegraph. Also credited at BrainyQuote.) However, as JJJ kindly points out, there are previous instances of its use, an earlier form being used by none other than Edward Murphy in the Washington Post in 1911. [cited in 'Behold the Proverbs of a People: Proverbial Wisdom in Culture, Literature ...' By Wolfgang Mieder].
Don't embarrass yourself any further.
John, just shut up. Don't embarrass yourself any further!
"Doubling down" is when you've said something, you're wrong, someone points it out, and you just keep on going instead of admitting your mistake.
"Digging your own grave" is similar, used when you've said or done something foolish or wrong and you try to get yourself out of the situation but instead just keep making it worse.
Here are a couple of related alternatives:
You'd better cut your losses. This doesn't have as close a meaning as the "stop digging" answer, but it's pretty common.
You've already made things bad enough for yourself. Stop now and cut your losses.
Similarly, when someone takes action to stop losses, this can be called stopping the bleeding.
Things are getting worse. We need to stop the bleeding.
When you make the worst of an already bad situation, you add insult to injury.
To add insult to injury is to make a bad situation become worse by saying or doing something.
He returned to the buffet for seconds, adding insult to injury.
If you try to explain why you're drunk, you'll only add insult to injury.
To add insult to injury, she refused to drop the subject.
Buttering the burnt toast added insult to injury.
Better to remain silent and be thought a fool than to speak and to remove all doubt.
My first thought was "putting the other foot in your mouth", as well but that may be more related to doing or saying something embarrassing that outright stupid.
Add fuel to the fire - to make a problem worse; to say or do something that makes a bad situation worse; to make an angry person get even angrier.
"'Tis better to be considered the silent fool than to open ones mouth, and remove all doubt ! " This, or some very similar phrase is an old one which never becomes an ineffective or irrelevant platitude. I believe its sums up the 'gist' of your saying as well. addendum: haha... as soon as i posted i read the post above mine.. and got 'dittoed'
"You've made your bed, now lie in it."
Meaning you made a mistake or done something silly and now you must deal with the consequences.
Ok... so I'll compose one too.. " Despite being an epic distraction, placing the other foot in your mouth as well leaves you quite unable to make a graceful exit, unless.... Um.. never mind, even "This Old Man" had to endure Knick-Knacks, Police brutality, and finding a bone to avoid a bite from Paddy's dog, before he was able to come 'Rolling Home' also legendarily ungraceful !"
I suppose my attempt would be better served as an English adage to your original saying if it ended at 'graceful exit.'.. but then "This Old Man" came to mind so i embellished some. I do, of course, usually strive for concision, if possible, when offering a suggestion or an answer, contrary to this tangentially rambling digressive explanation. haha