Do I have to pay a penalty if my former employer refunded my retirement account automatically when I quit?

If you did not roll over the retirement account to another tax deferred retirement account within 60 days then you will owe a 10% early distribution penalty.  The penalty is assessed on your federal tax return, Form 1040.

And this was not a "refund" of your retirement contributions.  It was a distribution due to the balance in the plan being below the threshold where the plan would be required to maintain the account.  It is taxable and subject to an early-distribution penalty if it was not rolled over as described by DoninGA.  This money consists of earnings on which you have not previously paid taxes, so it is taxable when distributed.

Your employer was required to have provided to you instructions regarding the tax consequences of this distribution prior to making the distribution unless you waived that requirement.  those instructions would have included your option to request a direct rollover to an IRA or other qualified retirement account to be able to continue to defer this income.