A B737-300 CREW HAVE A YAW DAMPENER THAT FAILED ON PUSHBACK MEL'ED BEFORE TAKEOFF.

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TODAY I RECEIVED A CALL FROM OUR ASSISTANT CHIEF PLT. HE CALLED TO TELL ME THAT WE WERE PROCEDURALLY INCORRECT IN THE WAY THE CAPT AND I HANDLED AN MEL SITUATION IN ZZZ YESTERDAY MORNING. THE CAPT AND I BOTH INTERPED AND THOUGHT THAT ONCE AN ACFT WAS OFF THE GATE AND READY FOR TAXI; THAT THE PROGRESSION OF FLT WAS INITIATED AND THEREFORE A YAW DAMPER FAIL LIGHT THAT ILLUMINATED COULD BE MEL'ED UPON ARR. THE ACP TOLD US THAT OUR MEL SHOULD HAVE BEEN TAKEN CARE OF PRIOR TO TKOF AND THAT INITIATION OF FLT IS CONSIDERED WHEN THE THRUST LEVERS ARE PUSHED FORWARD FOR TKOF ROLL. THIS BEING THE CASE; WE INADVERTENTLY DID NOT FOLLOW SOP. OUR MISSTEP OCCURRED DUE TO OUR MISINTERP OF PROCS STATED IN THE FOM AND WHAT CONSTITUTES MOVEMENT FOR THE PURPOSE OF FLT. TAKING A LITTLE EXTRA TIME ON THE GND IN ZZZ AND ERRING ON THE SIDE OF CAUTION WOULD HAVE ALLEVIATED THE WHOLE ISSUE. SUPPLEMENTAL INFO FROM ACN 811409: I THOUGHT THAT AFTER YOU WERE ON YOUR OWN PWR; YOU STAYED WITH THE QRH. AFTER ARRIVING IN ZZZ1; MAINT FIXED THE YAW DAMPER. MAKE IT MORE CLR IN THE FOM ABOUT THIS PROB.