AN AT43 CREW; AFTER LNDG AT EWR; MISSED EXITING THE RWY WHERE ATC EXPECTED; CAUSING SOME TXWY CONGESTION.

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AFTER LNDG ON RWY 11 IN EWR; THE TWR TOLD US TO 'MAKE A R; R TURN ON TXWY W THEN CALL YOUR RAMP.' MY FO DID NOT ACKNOWLEDGE RIGHT AWAY. I TOLD HIM IT WAS FOR US. THE TWR REPEATED THE SAME INSTRUCTIONS. AT THIS TIME; WE WERE APCHING TXWY R. DEPARTING ACFT USE TXWY R FOR INTXN TKOFS ON RWY 22R AT TXWY W. I BELIEVE THE CTLR THOUGHT WE WERE MAKING TXWY S; LOCATED BEFORE TXWY R. WHEN WE PASS TXWY S; THE TWR USUALLY ORDERS US TO MAKE A 180 DEG TURN ON RWY 11 AND TO CLR AT TXWY S. AS I TURNED ON TXWY R; WE WERE SOON FACING THE A320 WAITING FOR TKOF ON RWY 22R. THEY HAD THEIR TAXI LIGHT ON AND IT WAS VERY DIFFICULT TO JUDGE THE DISTANCE. I THOUGHT THE TWR KNEW WE WERE ON TXWY R AND THE AIRBUS WAS FAR AWAY. THEY FINALLY TURNED THEIR LIGHTS OFF AND I DISCOVERED WE WERE PRETTY CLOSE TO EACH OTHER. WE WERE ABLE TO MANEUVER AROUND EACH OTHER WITHOUT INCIDENT. THE CTLR THEN ASKED US OUR POS. WE SAID TXWY R. A SILENCE CONFIRMED WHAT I HAD THOUGHT. CONTRIBUTING FACTORS: 1) LAST LEG OF A 12 HR DUTY DAY. 2) NIGHT CONDITIONS. 3) MY FO NOT RESPONDING TO TWR (HE LATER TOLD ME HE HAD HIS VOLUME ALL THE WAY DOWN). 3) THE CTLR NOT STATING 'R ON TXWY S;' BUT SIMPLY 'R TURN.'