Fast ion effects on turbulence-driven zonal flow generation are investigated in the context of a simple reduced model based on the Hasegawa-Mima equation. Fast ions' much higher characteristic frequency of parallel motion in comparison to the drift wave's phase velocity along the magnetic field facilitates a derivation of the reduced model equations. Nonlinear mode coupling analyses show that the threshold amplitude of drift wave required for the zonal flow modulational instability is significantly reduced, making its generation easier. This occurs as a down-shift of the drift wave's frequency and a reduction of dispersion in the presence of the fast ions cause a decrease of the mismatch between the primary drift wave frequency and the zonal flow modulated sideband drift wave's characteristic frequency. This finding could be a common nonlinear physics mechanism behind numerous recent results on tokamak plasma confinement enhancement caused by the fast ions.