Physical layer security (PLS) is promising for secure short-packet transmissions in ultra-reliable and low-latency communications. The bottlenecks of applying PLS in practice include 1) lack of accurate channel state information (CSI) of both the intended user and the eavesdropper; 2) high computational complexity for solving optimization problems. To address the first issue, we compare the secure transmission rates of short packets in different scenarios (i.e., with/without eavesdropper’s instantaneous CSI and with/without channel estimation errors) and derive the closed-form optimal power control policy in a special case. To find numerical solutions in general cases, we apply an unsupervised deep learning method, which has low complexity after the training stage. Through numerical results, we obtain the following three key findings: 1) The learning-based power control policy approaches the closed-form optimal policy in the special case and outperforms two existing power control policies in general cases. 2) Knowing the instantaneous CSI of the eavesdropper only provides a marginal gain of the secure data rate in the high signal-to-noise ratio regime. 3) In the presence of channel estimation errors, the learning-based policy trained by the estimated channels can guarantee the average transmit power constraint, while the closed-form policy cannot.