The detection of weak radioactive sources in fluctuating background environments is a critical task for nuclear security, environmental monitoring, and emergency response. Compact gamma-ray detectors, such as small-volume CdZnTe (CZT) crystals, are well suited for portable and drone-mounted applications, but their limited active volume yields low-count spectra over short acquisition times. While most radiation detection systems can acquire spectra over short integration times, the key challenge is whether such brief acquisitions from compact detectors provide sufficient statistical information for reliable anomaly detection. In this work, we present an anomaly detection approach based on a convolutional autoencoder trained exclusively on background gamma spectra. The detector used is a 0.5cm³ CZT device that records 1024-channel spectra in operational low-count regime from short acquisitions. To provide probabilistic decision-making, Bayesian inference is applied to map reconstruction errors to anomaly probabilities. The method is evaluated on real spectra containing background alone and source-plus-background combinations for Cs-137, Am-241, and Eu-152 at varying source–detector distances. Results show that the autoencoder detects anomalies at source–detector distances where total counts overlap strongly with background and conventional Currie-type thresholds fail. Compared to the total counts method, the autoencoder achieves higher sensitivity, detecting weak Cs-137 anomalies at distances up to 50cm. These findings demonstrate that deep-learning methods can enhance the performance of compact detectors, enabling practical, mobile radiation monitoring systems with improved sensitivity in real-world operational scenarios.