Seems you are driving with H-Shifter & Manual clutch, there is nothing wrong with this by the way.
You are shifting WAY too slow. You actions on the clutch are somewhat, sloppy, you want to be rapid, but smooth at the same time. The lines you take around the track are no where near optimal, they are way off. Perhaps you could try using the LFS Default racing line provided when pressing the '4' key on your keyboard, just as a rough guide.
I dont think its so much as setup problems, only that you are lacking in experience.
Try watching the current world record for this combo, it should give you a great insight as to the line you take on corner entry, middle and exit, not forgetting braking and acceleration points.