An SR22T pilot departing TEB VFR entered NY Class B airspace; evidently expecting more help from TEB Tower.

Narrative

On the ground at TEB; I spoke to TEB Clearance to obtain VFR clearance to the north on departure. I requested 3;500 FT or 1;700 FT on departure. TEB Clearance put in and gave me 2;500 FT on departure; and gave me a discrete transponder code. TEB Tower cleared me for takeoff and right downwind departure off Runway 24. I proceeded to climb out on the downwind to 2;500 FT. While level at 2;500 FT and just prior to leaving TEB airspace; the TEB Tower Controller notified me that I was in the New York Class B airspace and to contact New York Approach at 120.80 (the departure frequency I had been given prior to takeoff). I immediately departed the Class B to the north and contacted 120.80. No further mention was made of any airspace violation. I am filing due to concern over the lack of communication between TEB Clearance and Tower and the warning that Tower gave regarding a Class B violation; when I was flying the instructions provide by Clearance. I do not believe that any safety issues arose due to this event; other than faulty communication. The remainder of the flight was uneventful.