Single-cell experiments of simple regulatory networks can markedly differ from cell population experiments. Such differences arise from stochastic events in individual cells that are averaged out in cell populations. For instance, while individual cells may show sustained oscillations in the concentrations of some proteins, such oscillations may appear damped in the population average. In this paper we investigate the role of RNA stochastic fluctuations as a leading force to produce a sustained excitatory behavior at the single-cell level. As opposed to some previous models, we build a fully stochastic model of a negative feedback loop that explicitly takes into account the RNA stochastic dynamics. We find that messenger RNA random fluctuations can be amplified during translation and produce sustained pulses of protein expression. Motivated by the recent appreciation of the importance of noncoding regulatory RNAs in post-transcription regulation, we also consider the possibility that a regulatory RNA transcript could bind to the messenger RNA and repress translation. Our findings show that the regulatory transcript helps reducing gene expression variability both at the single-cell level and at the cell population level.