Quasi-random nanostructured material systems (NMSs) are emerging engineered material systems via cost-effective, scalable bottom-up processes, such as the phase separation of polymer mixtures or the mechanical self-assembly based on thin-film wrinkling. Current development of functional quasi-random NMSs mainly follows a sequential strategy without considering the fabrication conditions in nanostructure optimization, which limits the feasibility of the optimized design for large-scale, parallel nanomanufacturing using bottom-up processes. We propose a novel design methodology for designing quasi-random NMSs that employs spectral density function (SDF) to concurrently optimize the nanostructure and design the corresponding nanomanufacturing conditions of a bottom-up process. Alternative to the well-known correlation functions for characterizing the structural correlation of NMSs, the SDF provides a convenient and informative design representation to bridge the gap between processing-structure and structure-performance relationships, to enable fast explorations of optimal fabricable nanostructures, and to exploit the stochastic nature of manufacturing processes. In this paper, we first introduce the SDF as a non-deterministic design representation for quasi-random NMSs, compared with the two-point correlation function. Efficient reconstruction methods for quasi-random NMSs are developed for handling different morphologies, such as the channeltype and particle-type, in simulation-based design. The SDF based computational design methodology is illustrated by the optimization of quasi-random light-trapping nanostructures in thin-film solar cells for both channel-type and particle-type NMSs. Finally, the concurrent design strategy is employed to optimize the quasi-random light-trapping structure manufactured via scalable wrinkle nanolithography process.