This study examined the effects of a decrease in thickness of magnetic alloy flakes on the electromagnetic wave absorption characteristics of nanocrystalline $Fe_{73.5}Cu_1Nb_3Si_{15.5}B_7$ (at.%) alloy flakes/polymer composite sheets available for a quasi-microwave band. The thickness of FeCuNbSiB alloy flakes decreased to 1-2 $mu$m with increasing milling time up to 24 h, and the composite sheet including alloy flakes milled for 24 h exhibited considerably enhanced power loss properties in the GHz range compared to the sheets having non-milled alloy powders. Although a considerable increase in loss factor upon milling was observed in the narrow frequency range of 4-6 GHz, there was no correlation between the complex permeability and flake thickness. However, the complex permittivity increased with increasing milling time, and there was good agreement between the milling time and the frequency dependences of the complex permittivity and power loss.