In this work, we propose a novel algorithm for subchannel and power allocation for Internet of Things (IoT) networks using downlink multicarrier nonorthogonal multiple access (MC-NOMA). Unlike single-carrier NOMA, MC-NOMA can utilize multiple subchannels, which is more suitable for supporting the massive connectivity of IoT users. However, in MC-NOMA, the joint subchannel and power allocation problem leads to a mixed-integer nonlinear programming problem, which is challenging to find an optimal solution. Therefore, in this article, we reformulate the joint subchannel and power allocation problem into a binary decision problem for subchannel allocation with a mathematical analysis of power allocation. Then, using the transformed problem, we propose a subchannel allocation scheme for MC-NOMA to improve the sum rate and outage performances compared with the conventional approaches. Even though many prior studies on the power allocation for MC-NOMA focused on deep learning-based methods to achieve an optimal solution with low complexity, it is difficult to jointly optimize the maximum power of each subchannel and the power for each NOMA user. Thus, we propose a deep learning-based training algorithm to optimize the maximum per-subchannel power with a mathematical analysis of power allocation for NOMA users. In addition, we introduce the user selection algorithm to avoid performance loss due to an outage user, where the presented algorithm can select users satisfying the data rate requirement. Through simulations, we show that the proposed subchannel and power allocation schemes have outstanding sum rate and outage performances compared with the existing schemes.