The phenomenon of fluorescence concentration quenching, when fluorescence quantum yield decreases upon increase of fluorophore concentration, has been studied for several decades. To this day, however, there is no unified understanding of its relationship with molecular aggregation and the origin of quenching centers. Unfortunately, high concentrations of fluorophores in solutions result in inner filter effects in fluorescence measurements. Therefore, in this work, we focus on fluorescence of Zinc 2,9,16,23-tetra-tert-butyl-29H,31H-phthalocyanine thin films. We observe signatures of concentration quenching at high concentrations. Our time-resolved measurements demonstrate change in the behavior of the fluorescence kinetics from the mono- to the multi-exponential decay. We construct an effective theoretical model, based on energy transfer between fluorescing donor and dark trap molecules, to explain the observed kinetics. Our description of the quenching kinetics is consistent with the well-known statistical pair model.