Turbulence models in Reynolds-Averaged Navier-Stokes simulations have a crucial effect on the compressor stability boundary. In this paper, the parametric uncertainty of the Spalart-Allmaras turbulence model on compressor flows is quantified by a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within intervals, and the quantities of interest include the Reynolds stress distribution, the shock front location and pressure coefficient and the separation size. An artificial neural network from machine learning is applied as the metamodel, which is tuned, trained, and tested by databases from the flow solver to achieve an error below 1% of the database range. The uncertainty of quantities of interest is determined by the range of the metamodel and the database samples from the flow solver. The sensitivity of model coefficients is quantified by calculating the gradient of quantities of interest from the metamodel. Results show that the measured data of Reynolds stress profiles in separated regions, shock front location and pressure coefficient and shock-induced separation size cannot be well captured. Crucial model coefficients on the quantities of interest are identified by a sensitivity analysis. However, re-calibration of these coefficients is contradictory in different quantities of interest and flow regimes. It indicates the need for a modified Spalart-Allmaras turbulence model form to improve the accuracy in predicting compressor flows.