Embraer Jet Undifferentiated or Other Model
Flight Crew Air Transport Pilot (ATP); Flight Crew Multiengine; Flight Crew Instrument
Workload; Situational Awareness; Distraction
Deviation - Altitude Overshoot; Deviation / Discrepancy - Procedural Clearance; Inflight Event / Encounter Wake Vortex Encounter
Air Traffic Control Issued New Clearance; Flight Crew Became Reoriented; Flight Crew Returned To Clearance
Environment - Non Weather Related; Human Factors; Procedure
As we were cleared to descend to 3000 ft into DFW we encountered moderate wake turbulence around 7500 ft that forced to use TCS [Touch Control Steering] to maintain control of the aircraft. We were giving clearance to level off at 6000 ft and turn to the left. As we were busy maintaining control of the aircraft we forgot to set 6000 ft in the altitude selection and ended up noticing it at 5400 ft. We checked with Approach and were told that we were supposed [to] level at 6000 ft but now level at 5000 ft. After we landed we called ATC to make sure everything was fine and was told it was a nonevent and we shouldn't worry about it. During a high work load of trying to maintain a positive control on the aircraft; we failed to comply with ATC instructions but tried our best to maintain aircraft control. Always cross check and verbalize that the flight crew is following the proper ATC instructions and if any doubt always double check with ATC.
[Report narrative contained no additional information]
EMB flight crew reported overshooting a cleared altitude after encountering wake turbulence on arrival into DFW.