B757 FLT CREW DEPARTED THE ACFT WITH AN ENGINE STILL RUNNING.

Narrative

THE EVENT OCCURRED DUE TO BEING INTERRUPTED WHILE STARTING THE SHUTDOWN CHKLIST. BEING VERY NEW TO THE B757 MY MAIN FOCUS HAS BEEN ON THE FLOWS. THE PATTERNS ARE DIFFERENT FROM THE LAST ACFT I FLEW; THAT IS; THE FLOW AFTER THE ENGS ARE SHUT DOWN. I; THE CAPT; TAXIED INTO THE GATE WITH THE APU RUNNING. AFTER SETTING THE PARKING BRAKE; I SHUT DOWN THE L ENG. I PAUSED BEFORE SHUTTING DOWN THE SECOND ENG TO ENSURE THE APU PICKED UP THE LOAD. I WENT THROUGH THE REST OF THE SHUTDOWN FLOW WHILE WAITING FOR THE APU TO PICK UP THE LOAD FROM THE L ENG GENERATOR. WHILE STARTING THE SHUTDOWN CHKLIST THE FLT ATTENDANT CALLED THE FO ABOUT A SEAT BACK THAT WOULD NOT STAY UP TO ENTER INTO THE LOGBOOK. THE FO RELAYED THE INFO TO ME. AFTER THE INTERRUPTION I CONTINUED THE CHKLIST THINKING THAT BOTH ENGS HAD BEEN CONFIRMED SHUT DOWN. NOT REALIZING THE R ENG WAS STILL RUNNING I LEFT THE ACFT AND WALKED TO OPS TO CHK THE COMPUTER. WHILE THERE THE ASSISTANT CHIEF PLT INFORMED ME THAT BOTH ENGS HAD NOT BEEN SHUT DOWN. I THINK IT WOULD BE BENEFICIAL IF BOTH PLTS WERE ACTIVELY INVOLVED IN THE SHUTDOWN CHKLIST TO ADD ANOTHER BARRIER AGAINST HUMAN ERROR. THE GATE AGENT NOTIFIED THE CHIEF PLT. THE CHIEF PLT INFORMED ME THAT BOTH ENGS HAD NOT BEEN SHUT DOWN WHILE I WAS IN THE CREW ROOM. A MECH SHUT DOWN THE R ENG. AT THE REQUEST OF THE ASSISTANT CHIEF PLT I TOOK A DRUG AND ALCOHOL TEST. UNDER COMPANY POLICY THE FO IS NOT REQUIRED TO READ THE SHUTDOWN CHKLIST; TAKING HIM OUT OF THE LOOP.