Is the anyway that you can be accountable for not having put my 1095 A in the taxes for healthcare marketplace on my taxes?

yes.  you'll probably get a letter from the IRS asking for form 8562 and a copy of 1095A.   meanwhile they will probably hold up your refund and when they do send it, it will probably be different form what is shown on yor return.  you could even owe. 

Since you prepared your taxes yursel, no, TurboTax is not at all accountable for you not filling out your healthcare information.