CRJ700 flight crew reports reducing thrust to slow per ATC request at FL380. Adequate thrust is never reestablished but prior to stall warning full power (APR) was applied and a descent was initiated to regain airspeed resulting in a TCAS TA.

Narrative

Enroute ATC requested speed reduction in cruise flight (FL 380) to .77 Mach; after reducing power to slow; never reapplied adequate power; resulting in gradual downward airspeed trend. Prior to stall warning; full power (APR) was applied and a descent was initiated to regain airspeed. ATC was informed that a descent was necessary; but no emergency was declared; ATC asked if emergency existed; response was no; but we were too busy dealing with the aircraft to consider this question. We were told not to descend; but by this time the stick shaker had gone off intermittently and a descent was absolutely necessary (should have declared emergency); but were occupied flying the airplane. Received a TA on TCAS and a traffic call by ATC; had traffic in sight immediately. Aircraft speed was recovered; new clearance to FL260 was received and flight continued uneventfully to destination.[We] reduced power to slow aircraft [but] failed to adequately monitor airspeed during reduction [and] failed to immediately declare emergency when low speed situation occurred. Consistently and diligently monitor aircraft instrumentation at all times. Do not hesitate to declare emergency.