Real-time audio communications over IP have become essential to our daily lives. Packet-switched networks, however, are inherently prone to jitter and data losses, thus creating a strong need for effective packet loss concealment (PLC) techniques. Though solutions based on deep learning have made significant progress in that direction as far as speech is concerned, extending the use of such methods to applications of Networked Music Performance (NMP) presents significant challenges, including high fidelity requirements, higher sampling rates, and stringent temporal constraints associated to the simultaneous interaction between remote musicians. In this article, we present PARCnet, a hybrid PLC method that utilizes a feed-forward neural network to estimate the time-domain residual signal of a parallel linear autoregressive model. Objective metrics and a listening test show that PARCnet provides state-of-the-art results while enabling real-time operation on CPU.