B757 flight crew reports LE SLAT DISAGREE during approach. Crew accomplishes QRH procedure and lands with full flaps and slats using the ALTN FLAP and SLAT selector switches.

Narrative

Upon selecting flaps 1 degree for landing; we received the 'Leading Edge Disagreement' light on the forward instrument panel along with the associated EICAS message; 'Leading Edge Slat Disagreement.' At that time; I notified ATC we were not ready to commence the approach and I referenced the QRH to perform the 'Leading Edge Slat Disagreement -757' procedure. Upon execution of the procedure; the Leading Edge Slats and Trailing Edge Flaps extended normally using the alternate Slat/Flap system and we commenced the approach and landed. After arriving at the gate; aircraft maintenance was notified and the mechanical discrepancy was entered in the aircraft logbook. While stowing my QRH; it occurred to me that the 'Leading Edge Slat Disagreement' procedure is an emergency procedure. With that information; I realized that an emergency should have been declared with ATC for the QRH procedure that I just performed. After further review of the QRH procedure; I determined that I had landed with a flap setting that was greater than what was called for in the given situation; but one that is appropriate for normal slat/flap operations. During this event; by interpreting the procedure incorrectly; and selecting this inappropriate landing flap setting for the given situation; I did not think that declaring an emergency was necessary. As Captain; and Pilot Monitoring; I take full and sole responsibility for all of the errors that occurred during the execution of this procedure. I incorrectly interpreted the QRH procedure; made all of the selections of the associated switches and flap positions; and failed to declare an emergency for the given situation.