Cine Magnetic Resonance Imaging (MRI) allows for understanding of the heart's function and condition in a non-invasive manner. Undersampling of the $k$-space is employed to reduce the scan duration, thus increasing patient comfort and reducing the risk of motion artefacts, at the cost of reduced image quality. In this challenge paper, we investigate the use of a convolutional recurrent neural network (CRNN) architecture to exploit temporal correlations in supervised cine cardiac MRI reconstruction. This is combined with a single-image super-resolution refinement module to improve single coil reconstruction by 4.4\% in structural similarity and 3.9\% in normalised mean square error compared to a plain CRNN implementation. We deploy a high-pass filter to our $\ell_1$ loss to allow greater emphasis on high-frequency details which are missing in the original data. The proposed model demonstrates considerable enhancements compared to the baseline case and holds promising potential for further improving cardiac MRI reconstruction.