We theoretically study the transmission reduction of light passing through absorptive molecules embedded in a periodic metal slot array in a near infrared wavelength regime. From the analytically solved transmitted light, we present a simple relation given by the attenuation length of light at the resonance wavelength of the slot antennas with respect to the spectral width of the resonant transmission peak. This relation clearly explains that the control of the transmission reduction even with very low absorptive materials is possible. We investigate also the transmission reduction by absorptive molecules in a real metallic slot antenna array on a dielectric substrate and compare the results with finite difference time domain calculations. In numerical calculations, we demonstrate that the same amount of transmission reduction by a bulk absorptive material can be achieved only with one-hundredth thickness of the same material when it is embedded in an optimized Fano-resonant slot antenna array. Our relation presented in this study can contribute to label-free chemical and biological sensing as an efficient design and performance criterion for periodic slot antenna arrays.