Air carrier Captain reported at the completion of the flight that the required Special Permit document had not been checked.

Narrative

After loading was completed; I was briefed by the loadmaster that we had class 1 hazardous materials on board the aircraft. Paperwork was signed; and the flight was completed. This is my first flight I had completed as a Captain under (special permit) SP-7573; and after the flight was completed; I reread the manual parts dealing with 7573 and believe that the Department of Transportation (DOT) SP-7573 box was not checked on the paperwork.