Photoluminescence of composites containing carbon nanostructures is critical for many modern applications. Of particular significance are metamaterials capable of generating white light photoluminescence within a single structure, as the white luminescence usually needs separate red-green-blue emitters. This work provides an insight into the photoluminescent properties of a promising family of hierarchical metamaterials made of carbon nanocones in a silicon oxide matrix in view of their use as efficient single-layer white light emitters. The composites were prepared using a facile plasma-enhanced technology, followed by a thermal treatment. ATR-FTIR, Raman, SEM, and AFM microscopy and profilometry characterization confirmed the presence of silica and carbon nanocones. The advanced comprehensive photoluminescence studies conducted using solid-state Yb:KGW laser revealed a significant difference in photoluminescent properties for the composites containing sharp nanocones of similar parameters. A comprehensive morphological analysis performed using several analytical techniques including the 2D fast Fourier transform spectra, Hough distributions, spectral density function, and Minkowski functionals revealed the Minkowski boundary functional, ordering, and connectivity to be the most important morphological descriptors for the photoluminescent response. This study suggests that these morphological parameters play a critical role in defining the key properties of advanced metamaterials via the overlap of ψ functions and may therefore be targeted for informed material design and intelligent fabrication.