First, check that this is a genuine warning. Check it for the usual signs of a scam email (faked "from" address, links you to a website that does not end in .gov). Contact US immigration on a publicly available email or number (not by any contact that you were given in the warning) and check with them.  

If it turns out it is genuine, it is probably not as serious as you think. It's most likely just an administrative mixup.

When you contact immigration they will tell you what you need to do, but most likely if you simply give them the date and flight number when you left that will be the end of it.  They will almost certainly be able to verify that you were on that flight, and that will probably be the end of the matter.

Also remember that, even if for some reason they don't believe that you left on the flight you did, you don't need to prove you left on that flight, you only need to prove you left before the end of your legal stay, ten days from now. The easiest way to do that is probably to make some sort of visit to someone official, like a government office or the police or a lawyer, where your visit will be recorded and you can provide information. But something as simple as records of an everyday transaction will help - a few records of you using your credit card in your hometown is going to be evidence, and is probably good enough.