Cell-free networks outperform cellular networks in many aspects, yet their efficiency is affected by imperfect channel state information (CSI). In order to address this issue, this work presents a robust resource allocation framework designed for the downlink of user-centric cell-free massive multi-input multi-output (CF-mMIMO) networks. This framework employs a sequential resource allocation strategy with a robust user scheduling algorithm designed to maximize the sum-rate of the network and two robust power allocation algorithms aimed at minimizing the mean square error, which are developed to mitigate the effects of imperfect CSI. An analysis of the proposed robust resource allocation problems is developed along with a study of their computational cost. Simulation results demonstrate the effectiveness of the proposed robust resource allocation algorithms, showing a performance improvement of up to 30\% compared to existing techniques.