BAe 125 Series 800
Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Flight Crew Last 90 Days 30; Flight Crew Total 6450; Flight Crew Type 1500
Workload; Time Pressure; Human-Machine Interface; Distraction
Aircraft Equipment Problem Less Severe; Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance
Air Traffic Control Issued Advisory / Alert; Flight Crew Became Reoriented; Flight Crew FLC Overrode Automation
Aircraft; Chart Or Publication; Procedure
We were on [TEB8] departure from TEB. When the pilot flying engaged the autopilot it did not capture the imminent charted altitude restriction. The autopilot was immediately disengaged; and corrective action was taken. During that corrective action; ATC assigned a higher altitude of 3;000 MSL.To prevent this from happening again I will reduce the climb rate on initial departure prior to engaging autopilot [when I am the pilot flying]. When performing pilot not flying duties I will only complete the essential after take-off checklist items when there is a low altitude restriction and will monitor more closely aircraft condition before completing the checklist.
When the autopilot failed to capture a crossing restriction altitude on a TEB SID the flight crew was forced to manually attempt to return to the charted alititude.  ATC assisted by clearing them to a higher altitude.