This paper investigates a machine learning-based power allocation design for secure transmission in a cognitive radio (CR) network. In particular, a neural network (NN)-based approach is proposed to maximize the secrecy rate of the secondary receiver under the constraints of total transmit power of secondary transmitter, and the interference leakage to the primary receiver, within which three different regularization schemes are developed. The key advantage of the proposed algorithm over conventional approaches is the capability to solve the power allocation problem with both perfect and imperfect channel state information. In a conventional setting, two completely different optimization frameworks have to be designed, namely the robust and non-robust designs. Furthermore, conventional algorithms are often based on iterative techniques, and hence, they require a considerable number of iterations, rendering them less suitable in future wireless networks where there are very stringent delay constraints. To meet the unprecedented requirements of future ultra-reliable low-latency networks, we propose an NN-based approach that can determine the power allocation in a CR network with significantly reduced computational time and complexity. As this trained NN only requires a small number of linear operations to yield the required power allocations, the approach can also be extended to different delay sensitive applications and services in future wireless networks. When evaluate the proposed method versus conventional approaches, using a suitable test set, the proposed approach can achieve more than 94% of the secrecy rate performance with less than 1% computation time and more than 93% satisfaction of interference leakage constraints. These results are obtained with significant reduction in computational time, which we believe that it is suitable for future real-time wireless applications.