A B757 CROSSES RWY 4L AT EWR WITH AN ACFT BEGINNING ITS TKOF ROLL AFTER TAXIING ON WRONG RTE. HIGH WORKLOAD ROLLOUT AT THE END OF A LONG DAY.

Narrative

MADE AN UNEVENTFUL VFR/ILS APCH TO EWR RWY 4R. WAS SURPRISED DURING THE FLARE THAT THE 90 DEGS; 15 KT R XWIND BECAME QUITE TURBULENT. HAD TO WORK AT THE LNDG AND LANDED A LITTLE LONG FOR ME. DURING LNDG ROLLOUT AND WHILE IN THRUST REVERSE AND BRAKING (ON A ROUGH RWY AND XWIND) TWR GAVE US CLRING INSTRUCTIONS. MY FO READ BACK THE CLRNC. I WAS NOT CONCENTRATING ON TWR'S INSTRUCTIONS DUE TO MY HIGH WORKLOAD AT THE TIME OF COMPLETING THE LNDG. I REMEMBER HEARING THE TWR AND THE FO SAY 'CLRING L;' MAYBE ANOTHER L. I TURNED OFF AT HIGH SPD TXWY L; THEN L ON TXWY Y; I CALLED FOR THE 'AFTER LNDG' CHK AND PROCEEDED FORWARD ON TXWY Y. NEARING THE END OF RWY 4L I ASKED THE FO IF TWR HAD CLRED US TO CROSS RWY 4L. HE LOOKED UP AND SAID 'YES.' I LOOKED L AND DOWN RWY 4L AND NOTICED AN ACFT IN POS. IT APPEARED STATIONARY AT (10000 FT AWAY) I TURNED ON MY STROBE LIGHTS AS IT IS MY HABIT WHENEVER XING AN ACTIVE RWY; PWRED UP SOME AND SCOOTED ACROSS RWY 4L ON TXWY Y.AFTER WE CLRED RWY 4L AS WE TURNED L ONTO TXWY R; TWR CALLED AND SAID WE HAD MISSED TXWY P. THE FO AND I HAD A BRIEF DISCUSSION. HE ROGERED THAT AND WE RECEIVED TAXI INSTRUCTIONS TO THE GATE. WE WERE NOT CLRED TO CROSS RWY 4L IT TURNED OUT. ALSO; THE ACFT I THOUGHT WAS IN POS HAD JUST BEGUN HIS TKOF ROLL. I WAS WRONG TO CROSS RWY 4L WITHOUT HEARING AND UNDERSTANDING THE TWR CLRNC. THE TWR SHOULD NOT HAVE GIVEN THE CLRNC WHILE WE WERE IN THAT STAGE OF ROLLOUT.THE FO SHOULD NOT HAVE READ IT BACK. HE DOES NOT KNOW WHY HE RESPONDED TO MY QUESTION IN THE AFFIRMATIVE. SAFE SEPARATION HAD NEVER BEEN COMPROMISED (VERIFIED BY EWR TWR IN THEIR RPT TO ME 7 DAYS LATER). NO DEV BY DEPARTING ACFT WAS TAKEN. NO TWR ACTION WAS TAKEN. I DO NOT THINK THE CTLR SAW UNTIL WE WERE CLR. ARR AT EWR WAS THE END OF A 10 HR WORK DAY. FATIGUE MAY HAVE FACTORED IN SOME. WE BOTH HIT 'SINKERS' ENRTE TO EWR. I HAD WATER. FO HAD COFFEE. WE BOTH SEEMED TO PERK UP THOUGH.