A B737-700 ROLLED TOWARD A PUSHBACK TUG BECAUSE THE PUSHBACK CREW FAILED TO REQUEST ACFT BRAKES SET PRIOR TO THEIR DISCONNECT.

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THIS EVENT TOOK PLACE DURING PUSHBACK FROM THE GATE. COMS WAS ESTABLISHED BTWN THE COCKPIT AND TUG OPERATOR AND A PUSHBACK CLRNC WAS RECEIVED. DURING THE PUSH; THE TUG OPERATOR CLRED US TO START BOTH ENGS. WE STARTED BOTH ENGS; ADVISING THE GND CREW PRIOR TO EACH ONE; AND CONTINUED TO BE PUSHED BACKWARDS. WE THEN CAME TO A STOP; NOT QUITE ON THE TXWY AND STILL POINTING AT A 45 DEG ANGLE TOWARD THE TERMINAL. I COULD BARELY SEE THE TUG; AS IT WAS CANTED SEVERELY OFF THE LOWER FRONT R OF THE NOSE. I THEN ASSUMED THE PUSHBACK WAS COMPLETED AND WAS READY FOR THE CALL TO 'SET BRAKES.' THEN THE PUSH CONTINUED BY ACTUALLY PULLING THE NOSE AWAY FROM THE TERMINAL FOR SEVERAL FT AND THEN SLOWING SLIGHTLY. WE HEARD AND FELT A RUMBLING SOUND FROM THE NOSE GEAR AREA; WHICH WE THOUGHT WAS JUST ANOTHER CHANGE IN DIRECTION. IT WAS ACTUALLY THE CREW DISCONNECTING THE TUG WITHOUT SAYING A WORD TO ANYONE ABOUT ANYTHING. NOW; AS IT WAS HARD FOR ME TO SEE THE TUG; IT FELT AS IF WE MIGHT STILL BE MOVING; WHILE SIMULTANEOUSLY MY FO MADE A QUICK CALL TO MENTION WE WERE APCHING THE STATIONARY TUG. I APPLIED THE BRAKES AS A LOUD 'STOP THE AIRPLANE' CAME FROM THE TUG DRIVER. I THEN HAD WORDS WITH TUE TUG OPERATOR AND INFORMED HIM OF THE IMPORTANCE OF EXACT PROCS AND VERBAL COMS THAT WERE COMPLETELY ABSENT.