Understanding the fundamental performance limits of memory-limited decoders is of importance in designing practical decoders for resource-limited nano-networks. While some existing works do consider decoders with limited memory, to best of our knowledge, the tradeoff between memory and probability of error has not been studied in the literature. In this paper we make a first step by studying this tradeoff for a particular molecular communication system. A memory-limited, decision-aided decoder is proposed and shown to be near-optimal. The effect of the amount of memory on performance is characterized. This effect is specialized for the case of Molecular Concentration Shift Keying; it is shown that four bits of memory achieves nearly the same performance as infinite memory.