Supercontinuum generation in nanoscale all-normal dispersion optical fibers requires special attention concerning the input coupling of light due to the small core size. Preceding taper transitions along which the fiber core gradually decreases from microscale to nanoscale dimensions facilitates the input coupling regarding efficiency and stability. The influence of these taper transitions on the subsequent supercontinuum generation in the nanoscale optical fiber is discussed in detail and appropriate taper shapes with minimized influence are proposed.