ACR TURNS; EXITS THE RWY IN THE WRONG DIRECTION AT EWR; NJ.

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WE LANDED AT EWR AT XA05Z ON RWY 29. WE SELECTED RWY 29 BECAUSE OF STRONG XWINDS ON RWY 4R. THE COPLT WAS MAKING THE LNDG; AND DURING DECELERATION AND PLANNING ON EXITING ON TXWY BB; THE TWR TOLD US (AS I UNDERSTOOD IT) TO ROLL TO THE END. I ACKNOWLEDGED WITH THE FLT NUMBER ONLY; AND DID NOT READ BACK THE FULL INSTRUCTION; AS I RECALL. UPON REACHING THE END OF THE RWY; I STARTED A L TURN ONTO TXWY Z. WHEN WELL INTO THE TURN; THE COPLT SAID 'I THINK HE MIGHT HAVE SAID TO MAKE A R TURNOFF.' UPON EXITING THE RWY AT TXWY Z AND CONTACTING GND; WE WERE ADVISED THAT I HAD MADE AN ILLEGAL TURN OFF THE ACTIVE RWY. THE REASON WE WERE GIVEN THE R TURN BECAME EVIDENT AS THERE WAS AN ACFT ON TXWY W; WITH SEVERAL FIRE TRUCKS AROUND. I INDICATED TO GND THAT I MISSED THE R TURN INSTRUCTION. AT THE TIME THAT THE RWY EXIT INSTRUCTIONS WERE GIVEN; I WAS INVOLVED WITH AIRSPD CALLOUTS AND COMING OUT OF REVERSE; AND AT A POINT WHERE I WAS PREPARING TO TAKE CTL OF THE ACFT I WAS COMPLACENT ABOUT THE INSTRUCTIONS AND PROPER READBACK. I RUSHED TO ACKNOWLEDGE WITHOUT A CLR UNDERSTANDING OF THE INSTRUCTIONS. HOWEVER; I DO FEEL THAT IF THESE INSTRUCTIONS WERE GIVEN PRIOR TO LNDG WE COULD HAVE BETTER PREPARED FOR THE LNDG. SUPPLEMENTAL INFO FROM ACN 465520: I WAS THE FE. I PERSONALLY DO NOT RECALL HAVING HEARD A R TURN AT THE END; PERHAPS BECAUSE I WAS BUSY RUNNING PORTIONS OF THE AFTER LNDG TAXI CHKLIST AND SETTING UP THE OTHER RADIO TO OPS FREQ TO CONFIRM GATE ARR AND TAXI INSTRUCTIONS.