We explore the application of artificial neural networks (ANNs) for the estimation of atmospheric parameters (Teff, logg, and [Fe/H]) for Galactic F- and G-type stars. The ANNs are fed with medium-resolution (Δλ~1-2 Å) non-flux-calibrated spectroscopic observations. From a sample of 279 stars with previous high-resolution determinations of metallicity and a set of (external) estimates of temperature and surface gravity, our ANNs are able to predict Teff with an accuracy of σ(Teff)=135-150 K over the range 4250<=Teff<=6500 K, logg with an accuracy of σ(logg)=0.25-0.30 dex over the range 1.0<=logg<=5.0 dex, and [Fe/H] with an accuracy σ([Fe/H])=0.15-0.20 dex over the range -4.0<=[Fe/H]<=0.3. Such accuracies are competitive with the results obtained by fine analysis of high-resolution spectra. It is noteworthy that the ANNs are able to obtain these results without consideration of photometric information for these stars. We have also explored the impact of the signal-to-noise ratio (S/N) on the behavior of ANNs and conclude that, when analyzed with ANNs trained on spectra of commensurate S/N, it is possible to extract physical parameter estimates of similar accuracy with stellar spectra having S/N as low as 13. Taken together, these results indicate that the ANN approach should be of primary importance for use in present and future large-scale spectroscopic surveys.