Sounds like either the game doesn't recognize when you press the throttle or you just don't press the throttle.
Solution: Press the throttle.
Slightly inappropriate joke aside, make sure all controls are correctly mapped in the controls menu. If necessary, calibrate your gamepad or whatever controller you use. If you use the same button for upshift/downshift, you MUST press the throttle to upshift.
Other than that, I can't help much.