Regret is a strong word to use. I think you should mostly be fine. Unless you’re getting a pay cut. There are advantages as well as disadvantages to work at a post you’re overqualified for. The remuneration is the thing that comes into play the most. If you, unfortunately, have to take up a job at such a post, there are extremely high chances that you lose numbers from your salary. There are also chances your salary is higher for a lower post if you move from a small company to a Fortune 500 company.
If you are getting an overall raise, you should be happy, though your overqualification means that the company will work you to your max. Sometimes positions below your caliber are fun as you can be more efficient at your job and also be a better overall employee. You will regret being overqualified only if you are paid less and are being treated with contempt at the new place.