Some of the best PvP players fly with a keyboard and mouse.
The mouse is a pointing device and is since it's used with fingertip control, whereas a joystick is used with the wrist and elbow, I would suggest that it's possible to get a higher degree of control out of a mouse.
Homunculi images show just how much more processing power is dedicated to the fingers than the wrist or elbow:
http://3.bp.blogspot.com/-b00FM2uh-VU/UAZLpK9ft2I/AAAAAAAAAIQ/ARHLjar-TDo/s1600/motor_1.jpg.
With that said, there are some excellent pilots who use a HOTAS. I suspect that rather than you just being inherently bad at fighting in this game, you're missing some important part of the practice.
!. Do you put the throttle at 50% to maximise your turns?
2. Do you use boost properly in conjunction with directional thrusters to control your distance from your target?
3. Do you juggle pips properly? 4 pips to shields when taking fire!
4. have you mapped yaw to the mouse X axis and roll to the keyboard?
5. Are you getting jumped by multiple NPCs when running missions, or is this in RES combat?
Where is the genitalia in that pic?