If your return was accepted, there is no need to amend your return.
The state employer ID number is really only a bureaucratic convenience for your state's department of revenue; it's simply not an essential element to the correct filing and processing of a valid personal income tax return (either state or federal). Your state department of revenue is able to easily identify your employer from their 9-digit federal EIN. Returns will still go through just fine, as long as there are no other errors on your return.