Am I obligated to pay 26 days additional rent if I did not give proper notice?

Good question. In most states there are statutes and case law where if a tenant is required to give a certain period of notice as to move out and falls short, the tenant is not obligated to pay the entirety of rent for the following month due to the improper notice, only a pro-rated protion of it.

To be in the safe side, carefully read your written lease assuming you have one for your rental. Its conditions control the obligations owed to you by the landlord and vice versa in the absence of conflicting state law.

I would send a follow up letter to your landlord confirming your last day at the rental and the circumstances for the ending of your rental and see what the response it thinking that you will have to pay a pro-rated portion for the subsequent month's rent. In the future, make sure you give written notices to your landlord. You could have mailed a copy of the notice or slipped it under the landlord's door.