FLC OF A B737 FAILED TO CONTACT GND CTL AFTER LEAVING THE RWY CAUSING MUCH GRIEF TO THE TWR GND CTLR BY NOT BEING ABLE TO COM WITH THE FLC DURING TAXI TO GATE.

Narrative

AT THE END OF THE LNDG ROLL; I TAKE CTL AND TURN R OFF THE RWY WHILE THE FO TAKES OVER THE RADIOS. THIS IS OUR HOME BASE; SO WE ARE VERY FAMILIAR; WE ARE VERY TIRED; AND THE FO IS AS EXPERIENCED AS I AM; PLUS WE HAVE JUST FINISHED THE LAST LNDG OF THE TRIP -- ALL OF THE ABOVE LEADING TO A VERY MSPLACED COMPLACENT FEELING ON MY PART. AS WE TURN OFF; I ASK THE FO WHICH WAY WE WERE CLRED TO TURN (THERE ARE 2 CHOICES; BOTH COMMONLY USED). HE SAYS 'R TURN; CLRED TO THE RAMP.' I THOUGHT THAT THIS MIGHT BE A NORMAL CLRNC AT A NON PEAK TIME; BUT NOT AT RUSH HR. HOWEVER; I CONTINUE FOLLOWING THE ACFT TAXIING AHEAD. AS WE APCH A XING HIGH SPD TURNOFF FROM THE ACTIVE; I AGAIN ASK THE FO 'ARE WE CLRED TO CROSS TXWY B?' AND HE SAYS 'YES; CLRED TO THE GATE.' A LNDG B757 FORTUNATELY IS GOING TOO FAST FOR THE HIGH SPD TURNOFF; SO THERE IS NO CONFLICT. AS WE APCH THE RAMP AND THE FO CALLS RAMP CTL; THEY STATE 'IS THAT YOU ON TXWY M?' OUR CONFIRMATION THAT ALL IS NOT WELL. THE FO VERIFIES THAT IT IS US; AND RAMP REPLIES WITH 'TAXI TO THE GATE; AND CALL THE FAA AT EXT XXXX.' UH OH. I CALLED GND; AND THEY SAY THEY TRIED US ON 4 RADIOS; AND I ADMITTED THAT WE JUST FLAT FORGOT TO CALL. THEY SAID THERE WOULD BE NO FURTHER ACTION; BUT TO TAKE CARE IN THE FUTURE.