FALSE EMER ALERT FROM EICAS DISTRACTS PLTS OF GLF4 FROM FLYING THE JET AND AN ALT EXCURSION RESULTS.

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MY HIGHLY EXPERIENCED FO WAS HAND FLYING; AUTOPLT AND AUTOTHROTTLES OFF. CLB WAS BEING CONDUCTED AT A HIGH RATE/SLOWER AIRSPD THAN NORMAL IN AN EFFORT TO CLB ABOVE CONTINUOUS MODERATE TURB. ATC DIRECTED A LEVELOFF AT 13000 FT MSL. MY FO LEVELED AT 13000 FT AND BEGAN TO ACCELERATE TO OUR TURB PENETRATION SPD OF 270 KTS. AT THIS TIME; THE EICAS SOUNDED A MOMENTARY; FALSE 3 BONG; RED; EMER ALERT. THIS IMMEDIATELY GOT BOTH OF OUR ATTNS. IT ONLY TOOK A SECOND OR 2 FOR ME TO REALIZED THE ALERT WAS FALSE; BUT THAT WAS ENOUGH FOR US TO CLB TO 13300 FT. I CALLED THE ALT TO MY FO AND HE IMMEDIATELY CORRECTED. WE TOPPED OUT AT ABOUT 13375 FT. FORTUNATELY THERE WERE NO TFC CONFLICTS. MODERATE TURB; ACFT PERFORMANCE (WE HAD A CLB RATE EXCEEDING 6000 FPM TO THIS POINT); NON USE OF AUTOMATION; AND THE HUMAN FACTORS INVOLVED WHEN A PIC HAS MUCH MORE EXPERIENCE IN TYPE; BUT FEWER YRS TOTAL EXPERIENCE THAN THE SIC; PLAYED A PART IN THIS INCIDENT. I BECAME COMPLACENT AND DID NOT RECOMMEND A MODERATION OF THE CLB RATE AS WE NEARED LEVELOFF OR THE USE OF THE AUTOTHROTTLES. AS A RESULT; MY FO NEEDED TO AGGRESSIVELY TRIM THE NOSE DOWN TO AVOID A CLB DURING OUR LEVELOFF AND ACCELERATION. THE EICAS ALERT BROKE HIS CONCENTRATION ON THIS TASK; AND THE TURB NEGATED THE 'SEAT OF OUR PANTS' FEEL WHICH MAY HAVE ALERTED US TO OUR UNINTENDED CLB.