What do you do if you are caught red handed on video tape saying something that is completely and factually wrong?
My recommendation to you is that you admit what you said was wrong, say what is the correct answer, have an appropriate level of remorse in your tone, and since it really is not that big of a deal, don’t make too much of a deal out of it. If it is truly significant and you have harmed people, then a more thorough apology is in order.
If you don’t do this, you are going to destroy your credibility even more and you are only going to appeal to people who don’t believe in rational facts or thoughts. If that is your audience, then be my guest. But if you have customers and clients and employees or voters or anyone you care about and they can see that you said something incredibly wrong, own up to it.
Do not wait until a lot of people put pressure on you, come out quickly. In this way, your credibility will be restored.