No, you don't need a clutch. 😉 The clutch is automatically operated. However, sometimes it gets stuck after crashing. It doesn't happen to me anymore, but maybe it does on your system.
Do you play the downloadable version, or the web version?
Does it usually happen after a few crashes?
Does the car stil rev, but without accelerating?
The gear gets stuck if I'm correct? Or does it still go up and down?
Try turning on the pedal bars anyway. If the blue bar is full, the clutch is stuck in the open position.