We report on a systematic investigation of the γ-ray properties of 120 hard X-ray-selected Seyfert galaxies classified as "radio-quiet" objects, utilizing the three-year accumulation of Fermi Large Area Telescope (LAT) data. Our sample of Seyfert galaxies is selected using the Swift Burst Alert Telescope 58 month catalog, restricting the analysis to the bright sources with average hard X-ray fluxes F 14 - 195 keV >= 2.5 × 10-11 erg cm-2 s-1 at high Galactic latitudes (|b| > 10°). In order to remove "radio-loud" objects from the sample, we use the "hard X-ray radio loudness parameter," R rX, defined as the ratio of the total 1.4 GHz radio to 14-195 keV hard X-ray energy fluxes. Among 120 X-ray bright Seyfert galaxies with R rX <10-4, we did not find a statistically significant γ-ray excess (TS > 25) positionally coincident with any target Seyferts, with possible exceptions of ESO 323-G077 and NGC 6814. The mean value of the 95% confidence level γ-ray upper limit for the integrated photon flux above 100 MeV from the analyzed Seyferts is ~= 4 × 10-9 photons cm-2 s-1 , and the upper limits derived for several objects reach ~= 1 × 10-9 photons cm-2 s-1 . Our results indicate that no prominent γ-ray emission component related to active galactic nucleus activity is present in the spectra of Seyferts around GeV energies. The Fermi-LAT upper limits derived for our sample probe the ratio of γ-ray to X-ray luminosities L γ/L X < 0.1, and even <0.01 in some cases. The obtained results impose novel constraints on the models for high-energy radiation of "radio-quiet" Seyfert galaxies.Read less <