We report here on results of systematic experimental-theoretical investigation of high-order harmonic generation (HHG) in layers of CdSe semiconductor quantum dots of different sizes and a reference bulk CdSe thin film. We observe a strong decrease in the efficiency, up to complete suppression of HHG with energies of quanta above the bandgap for the smallest dots, whereas the intensity of below bandgap harmonics remains weakly affected by the dot size. In addition, it is observed that the ratio between suppression of above gap harmonics versus below gap harmonics increases with driving wavelength. These systematic investigations allow us to develop a simple physical picture explaining the observed suppression of the highest harmonics: the discretization of electronic energy levels seems to be not the predominant contribution to the observed suppression but rather the confined dot size itself, causing field-driven electrons to scatter off the dot’s walls. The reduction in the dot size below the classical electron oscillatory radius and the corresponding scattering limits the maximum acceleration by the laser field. Moreover, this scattering leads to a chaotization of motion, causing dephasing and a loss of coherence, therefore suppressing the efficiency of the emission of highest-order harmonics. Our results demonstrate a new regime of intense laser-nanoscale solid interaction, intermediate between the bulk and single molecule response, and are crucial for nanophotonic platforms aiming control over high-order harmonic properties and efficiency.