Without knowing what the TurboTax program indicated for the reason why the state return could not be e-filed there is no way to answer that question.
When you print the tax return for mailing from the PDF download there will be mailing instructions for the state return.
Or go to this New York state Department of Taxation and Finance website for the mailing address for the NY state return with or without a tax payment - https://www.tax.ny.gov/pit/file/return_assembly_mail.htm
You will also need to include with the mailed return any 2021 W-2's or Form 1099's which have state income taxes withheld on the forms.
