When I filed with TurboTax I was under the impression that it would be automatically mailed out is this correct or not? If it isn't what can I do now since it's late?

Only you can print, sign, date and mail the tax return to the IRS.

You can also change to e-filing from mailing.  See this TurboTax support FAQ for changing from mail to e-file - https://ttlc.intuit.com/community/e-file/help/how-do-i-change-from-mail-to-e-file-in-turbotax-online/01/26985

There are no penalties for filing after the due date if there are no taxes owed or there is a tax refund.

Did you efile?  If you efile there is nothing to mail in.  You either efile or print and mail it yourself.

How to mail a return from the Online version

https://ttlc.intuit.com/community/printing/help/how-do-i-print-and-mail-my-return-in-turbotax-online/00/26258

Be sure to attach copies of your W2s and any 1099s that have withholding on them.  You have to mail federal and state in separate envelopes because they go to different places.  Get a tracking number from the post office when you mail them for proof of filing.

Do you think you efiled?  

You can check your efile status here     

https://turbotax.intuit.com/tax-tools/efile-status-lookup/   

When you efile you get back 2 emails.  The first email only confirms the transmission.  The second email says if the IRS (or state) Accepted or Rejected your efile.

When you log into your account you should also see the status and if it was Accepted or Rejected, Started, Printed, Ready to Mail, etc.  What does it say?