Measured Q factor of LC circuit does not correspond with calculated and simulated
My LC circuit consists of:
  
  L= 33,4 uH R= 0.3 Ω C=32,63 nF


Not quite true; there is also the 50 ohm impedance of the signal generator parallel loading the LC. You would need to drive this circuit differently i.e. with a current source if you wanted to measure Q factor: -



Resonant frequency is at 152.524 kHz and the 3 dB point is at 153.241 kHz. The upper and lower 3 dB bandwidth is therefore 1.434 kHz and the Q is centre frequency divided by bandwidth is: - 

$$\dfrac{152.524}{1.434} = 106.36$$


  In my opinion, the problem is just with measurements setup, but I do
  not know how to use a function generator for LC circuit, which has
  variable impedance.


Correct.