EMB145 FLT CREW TAXIED ON A CLOSED TXWY WHEN GOING TO THEIR GATE DURING A NIGHT OP AT PHL; PA.

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AFTER LNDG; PHL TWR INSTRUCTED US TO 'TAXI VIA TXWY K TO SPOT X; RAMP CTL IS CLOSED; TAXI TO THE GATE.' UPON ARRIVING AT SPOT X; WE TAXIED VIA TXWY J TO OUR GATE. AFTER ARRIVING AT OUR GATE; I REALIZED I TAXIED ON A CLOSED TXWY (ATIS RPTED 'TXWY J CLOSED BTWN TXWY Q AND TXWY N'). ALTHOUGH I WAS AWARE OF THIS CLOSURE PRIOR TO LNDG; I HAD IN MY MIND THAT IT WOULD NOT AFFECT OUR TAXI TO THE GATE SINCE ATC NORMALLY INSTRUCTS US TO TAXI TO SPOT Y (A SPOT JUST OUTSIDE OUR GATE AREA AND CLR OF THE CLOSED SECTION OF TXWY J). SINCE I REALIZED I WAS ON SPOT X (NOT SPOT Y) AND INSTRUCTED TO 'TAXI TO THE GATE;' I MISTAKENLY TAXIED ON A CLOSED SECTION OF TXWY J. CONTRIBUTING FACTORS FOR THE ERROR: 1) I WAS 'EXPECTING' SPOT Y INSTEAD OF SPOT X. I SHOULD NOT HAVE ASSUMED. 2) THE FLT CREW HAD JUST LANDED AFTER HAVING TO DIVERT TO EWR DUE TO TSTMS IN PHL AND TO GET MORE FUEL FOR A RE-DISPATCH TO PHL. WE WERE ON 'INFO OVERLOAD' DEALING WITH VERY SHORT DIVERSION FLTS; WX; FLT PLAN CHANGES; ETC. 3) PHL TWR THOUGHT OUR GATE WAS CLOSE TO SPOT X; WHICH IT WAS NOT. 4) NO CONES; BARRIERS; ETC; TO PHYSICALLY IDENT THE TXWY CLOSURE AND NOTHING WAS COMMUNICATED TO US FROM PHL TWR. 5) NIGHTTIME; TSTMS; HVY RAIN; RAMP WAS CLOSED. FLT CREW FLYING 9+ HRS THIS DAY IN CONSTANTLY CHANGING WX/FUEL CONSIDERATIONS. WE WERE TIRED AFTER LNDG. 6) PHL TWR WOULD NEVER HAVE GIVEN US SPOT X HAD HE REALIZED OUR GATE WAS CLOSE TO SPOT Y. I'M SURE HE WAS EXHAUSTED TOO.