Exciton energy transfer in organic whispering-gallery-mode (WGM) resonators and its effect on the amplified spontaneous emission (ASE) threshold have been investigated using the stilbene-based energy donor 4,4'-bis[(N-carbazole)styryl]biphenyl (BSB-Cz) and the coumarin-based energy acceptor 2,3,6,7-tetrahydro-1,1,7,7,-tetramethyl-1H,5H,11H-10-(2-benzothiazolyl)quinolizino[9,9a,1gh]coumarin (C545T). Using the stacked-layer structure of BSB-Cz/C545T/BSB-Cz, we fabricated bowl-shaped microresonators on silica microspheres with a total thickness of 250 nm fixing the thickness of the C545T layer to 1 nm. The ASE threshold depended on the thicknesses of the top and bottom BSB-Cz layers, which affect the magnitude of the energy transfer. To assess the relationship between the ASE threshold and energy transfer, we developed a device parameter to evaluate the magnitude of the energy transfer by formulating the rate equations. We found that ASE easily occurs under the condition that the C545T molecules become unable to accept energy from the BSB-Cz excitons owing to the high exciton density of C545T, and that the ASE threshold decreases with decreasing device parameter. The device parameter is useful for optimizing microresonator structures in multi-component organic WGM resonators that utilize energy transfer.