Cognitive radio (CR) has been introduced into the Internet of Things (IoT) domain as a potential solution to the critical spectrum resource shortage caused by a dramatic increase of IoT solutions within a limited operational spectrum. One technique of use within traditional CR processing for sensing communication activity across a spectrum of interest is automatic modulation classification (AMC). However, utilizing AMC within resource-limited cognitive radio-enabled IoT (CR-IoT) devices poses a significant challenge. In this article, we present a high-efficiency automatic modulation classifier architecture whose core is built upon the implementation of stacking quasirecurrent neural network (S-QRNN) layers acting as a feature extraction stage. This architecture utilizes the low-latency feature extraction capability of convolutional layers, and a minimalist recurrent pooling function that mimics recurrent-layer operations to aggregate the extracted features over time steps for higher classification accuracy. Additionally, implementing dense layers between two consecutive QRNN layers helps keep the network growth rate low. Therefore, the proposed S-QRNN classifier overall exhibits higher efficiency, fitting well within the limitations of CR-IoT devices. In order to demonstrate higher performance efficiency of our classifier, we conduct a comprehensive evaluation of our approach against the state-of-the-art AMC classifiers. Our analysis metrics of the classifier performance focuses on trainability, classification accuracy, execution latency, and resulting overall efficiency. Our results demonstrate that our proposed S-QRNN classifier exhibits higher trainability and, on average, a 75.83% higher efficiency, while it has, on average, a 26.54% lower execution latency. We then expand upon S-QRNN’s foundation by introducing gated recurrent units into our classifier to initially extract temporal features of the received constellations. The resulting GS-QRNN classifier demonstrates an efficiency increase by an average of 191% compared to the gated-enhanced recurrent-neural-network-based AMC classifier, with our GS-QRNN classifier average execution latency being 59.31% lower.