The problem of single-channel audio source separation is to recover (separate) multiple audio sources that are mixed in a single-channel audio signal (e.g. people talking over each other). Some of the best performing single-channel source separation methods utilize downsampling to either make the separation process faster or make the neural networks bigger and increase accuracy. The problem concerning downsampling is that it usually results in information loss. In this paper, we tackle this problem by introducing SFSRNet which contains a super-resolution (SR) network. The SR network is trained to reconstruct the missing information in the upper frequencies of the audio signal by operating on the spectrograms of the output audio source estimations and the input audio mixture. Any separation method where the length of the sequence is a bottleneck in speed and memory can be made faster or more accurate by using the SR network. Based on the WSJ0-2mix benchmark where estimations of the audio signal of two speakers need to be extracted from the mixture, in our experiments our proposed SFSRNet reaches a scale-invariant signal-to-noise-ratio improvement (SI-SNRi) of 24.0 dB outperforming the state-of-the-art solution SepFormer which reaches an SI-SNRi of 22.3 dB.