In cell-free massive multiple-input multiple-output (MIMO) networks, robust resource allocation is critical to ensure reliable system performance in the presence of channel uncertainties resulting from imperfect channel state information (CSI). In this work, we propose a robust power allocation method that formulates the power optimization problem into a least-squares framework, enhanced by Tikhonov regularization to mitigate the adverse effects of channel estimation errors. We integrate our approach with zero-forcing precoding, enabling a design that is both computationally efficient and resilient to CSI imperfections. Numerical results indicate that the proposed method outperforms existing non-robust techniques while benefiting from low computational overhead, making it well-suited for large-scale deployments under CSI uncertainty.