MD80 CREW FLIES TO NEAR STALL WHILE DEPENDING ON AUTOFLT.

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AFTER INTERMEDIATE LEVELOFF ON CLBOUT FROM PHX; RECEIVED CLRNC TO FL330. USED VERT SPD TO START CLB; THEN USED EPR LIMIT FOR THRUST SETTING. I BELIEVED I PUSHED IAS; BUT APPARENTLY DID NOT VERIFY THE FLT MGMNT ANNUNCIATOR. FROM THAT POINT ON; WAS DISTR AND DID NOT NOTICE AIRSPD DECAY SLOWLY FROM APPROX 300 KTS TO 210 KTS. BOTH FO AND I SUDDENLY NOTICED IT WAS GETTING QUIET; AND BOTH NOTICED LOW AIRSPD. SO I DISCONNECTED AUTOPLT; LEVELED OFF AT FL295; AND FO CALLED ATC TO REQUEST FL280. THEN DISCONNECTED AUTOTHROTTLES AND ADVANCED THRUST LEVERS; BUT DID NOT EXCEED EGT OR RPM LIMITS. FO NOTICED EPR'S WERE HIGHER THAN BUGS; SO I CALLED FOR MAX CONTINUOUS THRUST. AFTER ATC CLRED US FOR 280 KTS; I SLOWLY LOWERED THE NOSE AND ACCELERATED WHILE DRIFTING DOWN TO FL280. ONCE NORMAL AIRSPD ESTABLISHED; CONTINUED CLB TO FL330. DURING THE RECOVERY; NOTICED THAT ENG PWR LOWER ON R SIDE FOR SAME THRUST LEVER POS; SO TURNED ON ENG ANTI-ICE ONE AT A TIME DUE TO SUSPECTED PROBE ICING. THE ENG IMMEDIATELY RESPONDED BACK TO NORMAL INDICATIONS AND THRUST LEVERS WERE AGAIN ALIGNED NORMALLY. THERE ARE A COUPLE OF ITEMS TO BE NOTED: 1) THE TRAINING WE RECEIVE FOR THIS TYPE OF SIT IS PRETTY GOOD AND HELPED IN THIS CASE. 2) HOWEVER; UNLIKE TRAINING; DID NOT HEAR (OR NOTICE) THE CONSTANT AUTOPILOT TRIM HORN THAT LEADS UP TO THE EVENT. 3) WE SHOULD EMPHASIZE 'SLOW CTL MOVEMENT' AND EVEN THOUGH I EXERCISED THIS; I GOT THE SPD LOW FLT MODE ANNUNCIATOR ALERT AND A MOMENTARY BUFFET DURING THE RECOVERY.