Plasmonic or exciton/plasmon (plexcitonic) systems are presently described based on electromagnetic models, ignoring the need for an improved microscopic understanding. This is based on the fact that a full quantum mechanical approach on a micrometer scale still represents a considerable challenge. In this paper we report on the experimental observation of plexcitons in 2D gold nanorod array systems coupled to dye molecules and we provide a description of the experimental data using a quantum model. We show that treating the collective behavior in the array as being represented by a single quasiparticle is a suitable approximation that offers the opportunity to avoid the complicated calculation of long-distance interactions between the individual nanoparticles of the plexcitonic, periodic system. This enables us to model the optical response of plasmons in nanostructured arrays in contact with quantum emitters and to derive microscopic informations. Our work provides a potential tool for the design of plexcitonic devices, which rely on periodic metallic nanostructures.