A HARRIED DEP CTLR AT TEB INCORRECTLY ADVISED LR45 AIRCREW THEY HAD FAILED TO COMPLY WITH THE 1500 FT MSL RESTR ON THE TEB DEP OFF RWY 24.

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WITH THE EMPHASIS ON PROPERLY FLYING THE TEB 5 DEP; THE CAPT AND I REVIEWED THE PROC BEFORE ENGINE START AND BRIEFED THE PROC AGAIN BEFORE TKOF. AFTER BEING CLRED FOR TKOF ON RWY 24; WE CLBED ON RWY HDG UNTIL 1500 FT AND THEN TURNED R TO A 280 DEG HDG. WE WERE TOLD TO CONTACT DEP AND AFTER THE FREQUENCY CHANGE WE WERE LISTENING TO A VERY BUSY CTLR. UNABLE TO MAKE CONTACT DUE TO FREQUENCY CONGESTION WE CONTINUED THE DEP. AT THE TEB 4.5 DME FIX USING GREEN DATA (VOR) I REACHED UP AND TURNED THE ALT SELECT TO 2000 FT AND VERIFIED WITH THE CAPT THAT WE HAD CROSSED THE 4.5 DME OF TEB AND SHOULD CLB TO 2000 FT ON THE 280 DEG HDG. AGREEING I WAS ABLE TO CONTACT DEP AND TOLD HIM WE WERE OUT OF 1800 FT FOR 2000 FT. HIS REPLY WAS THAT WE COULD NOT CLB YET AND FLY THE DEP AND CONTACT NY ON 127.6. WE WERE ON 126.7 WHICH BRIEFLY MADE ME BELIEVE I WAS ON THE WRONG FREQUENCY WITH THE FIRST CTLR. CONTACTING 127.6 WE INDICATED LEVEL AT 2000 FT ON A 280 DEG HDG. WE WERE IMMEDIATELY CLRED TO COATE INTXN AND 10000 FT. NO MENTION WAS MADE OF ANY WRONG DOING ON OUR BEHALF. ONCE REACHING CRUISE ALT WE AGAIN REVIEWED THE DEP AND COULDN'T FIND FAULT WITH OUR PERFORMANCE. I FEEL THAT THE CTLR WAS BUSY AND HIS COMMENT HAD NO MERIT. IT IS FRUSTRATING WHEN WE AS PLTS ARE SECOND GUESSING OURSELVES IN BUSY ENVIRONMENTS WHICH I FEEL AFFECTS THE SAFETY OF THE FLT.