CAPT OF ACR MLG ACFT INADVERTENTLY TAXIED OFF THE TXWY DURING TAXI FOR TKOF.

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SAN-LAX. WE WERE SUPPOSED TO DEPART XY00 PST; BUT HAD RETURNED TO THE GATE FOR A MECHANICAL PROB. IT WAS MEL'ED AND WE PUSHED BACK AGAIN FROM GATE; 20 MINS LATE. WE HAD TIGHT CONNECTION FLTS IN LAX; SO I WAS IN A HURRY TO GET GOING. WE RECEIVED TAXI CLRNC TO RWY 27 FROM GND CTL AND I BEGAN TO SINGLE ENG TAXI. THE PARALLEL TXWY FOR RWY 27 IS UNDER CONSTRUCTION AND IS MARKED WITH FLASHING YELLOW LIGHTS AND STRIPED WOODEN TIES AS BARRIERS. 1 SET OF BLUE EDGE LIGHTS IS ALONG THE N SIDE OF THE TXWY. IT WAS NIGHT TIME. I BEGAN MY TAXI; FOLLOWING A YELLOW LINE AND STEERING BTWN THE BARRIERS. I TAXIED BY MISTAKE OFF THE TXWY INTO THE CONSTRUCTION ZONE BORDERED BY TXWYS F AND E; RWY 27 AND THE BARRIERS FOR THE MAIN TXWY. IT WAS MY CARELESSNESS AND HASTE WHICH CAUSED ME TO ENTER THIS AREA. IT HAS NEVER BEEN AN AREA TO TAXI AND I WAS LUCKY IT SUPPORTED MY WT. THERE WAS PLENTY OF ROOM WHERE I STOPPED AND A COMPANY TUG HOOKED UP AND PUSHED ME BACK ONTO THE TXWY. RWY 27 OPS WERE UNAFFECTED. I THINK IF THE BARRIERS AND LIGHTS WERE PLACED SO THAT IT WOULD BE IMPOSSIBLE TO TAXI THERE; THIS WON'T HAPPEN AGAIN. THIS MISTAKE WAS COMPLETELY MY FAULT; HOWEVER. MY FO WAS BUSY WITH WT AND BAL DATA; TRYING TO EXPEDITE OUR DEP. I'LL BE MORE CAREFUL WITH CONSTRUCTION.