Mechanic feeling rushed and under pressure to get their aircraft to the gate for on-time departures; failed to properly secure an APU oil cap. Mechanic noted the difficulty working too many Maintenance Tasks on too many aircraft due to lack of manpower; fatigue and too few qualified Taxi/Run mechanics for the workload expected to be accomplished.

Narrative

I was working a CRJ-200 aircraft August 2010 in the APU bay area; on the APU and other servicing routines for a Service Check and through maintenance for this aircraft. I had oil and fuel spillage in the [APU] bay area to clean up and had serviced the oil tank. I closed the cap on the oil tank and apparently thought the cap was on.I was bounced around other aircraft that night and had to come back to this aircraft to finish Leak and Run Checks which were good on the APU assembly. The aircraft had to go to the Run-Up [area] for engine runs and I was the only one qualified to Taxi and Run this aircraft. I felt that I was rushed to get aircraft out on time; delivered aircraft back to gate and went back to hangar to finish paperwork for this aircraft.Then I got a call to [to the] gate to Inspect oil servicing tank lid for security and found it loose; secured lid and found a rag behind the tank. Went to talk to the [Flight] Crew and told then I had secured the lid and found the rag. No documentation was noted in the Logbook; so I went back to the hangar and nothing was said. Too many projects started at one time; need to stay focused on task at hand. Jumping around to too many aircraft due to shortage of manpower. Feel that I am rushed under pressure due to gate times. Need more people to become more Taxi/Run qualified.