The ratio of orbital-to-spin magnetic moment μLeff/μSeff averaged over the element-specific contributions of Fe and Pt has been measured for 3-nm FexPt1-x nanoparticles at room temperature using the multifrequency electron paramagnetic resonance method for different concentrations of Fe. From a detailed g-factor analysis we determine that the ratio decreases from μLeff/μSeff=0.049 for x=0.43 to μLeff/μSeff=0.016 for x=0.70 which is much smaller than the bulk iron value (μLFe/μSFe=0.045). The observed concentration dependence is much stronger than the one calculated for FexPt1-x bulk samples and reveals likely changes of the confined electronic structure of the nanoparticle system. The ratio μLeff/μSeff takes the lowest value at the concentration (x=0.70) where the magnetic anisotropy energy vanishes in bulk alloys. For x>0.72 a phase transition from a fcc to the Fe bcc structure occurs resulting in the increased bulk ratio again.