The substrate effects on aperture resonance have been widely studied because the resonance peak position is key for sensing, communications, and field enhancement applications. So far, the theoretical works have focused on the lossless infinite substrate case, which only explains the resonance peak redshift by the substrate index. The loss effect has not been investigated yet because lossy infinite substrate significantly reduces the aperture transmission. Therefore, this work studied the loss effect on aperture resonance via an analytic model of the transmission though slot antennas on a finite substrate. When the substrate thickness was very thin compared to the wavelength, the transmittance remained high even for a large imaginary part of the refractive index; furthermore, the developed model predicted a strong blueshift when this imaginary part exceeds the real part. Besides, the zero of the imaginary part of the coupling strength was crucial in determining the resonance frequency for both infinite and finite substrates. Thus, this study can contribute to the material characterization, label-free detection, and efficient design of active metamaterials.