Automatic Sleep Staging study is presently done with the help of Electroencephalogram (EEG) signals. Recently, Deep Learning (DL) based approaches have enabled significant progress in this area, allowing for near-human accuracy in automated sleep staging. However, EEG based sleep staging requires an extensive as well as an expensive clinical setup. Moreover, the requirement of an expert for setup and the added inconvenience to the subject under study renders it unfavourable in a point of care context. Electrocardiogram (ECG), an unobtrusive alternative to EEG, is more suitable, but its performance, unsurprisingly, remains sub-par compared to EEG-based sleep staging. Naturally, it would be helpful to transfer knowledge from EEG to ECG, ultimately enhancing the model's performance on ECG based inputs. Knowledge Distillation (KD) is a renowned concept in DL that looks to transfer knowledge from a better but potentially more cumbersome teacher model to a compact student model. Building on this concept, we propose a cross-modal KD framework to improve ECG-based sleep staging performance with assistance from features learned through models trained on EEG. Additionally, we also conducted multiple experiments on the individual components of the proposed model to get better insight into the distillation approach. Data of 200 subjects from the Montreal Archive of Sleep Studies (MASS) was utilized for our study. The proposed model showed a 14.3\% and 13.4\% increase in weighted-F1-score in 4-class and 3-class sleep staging, respectively. This demonstrates the viability of KD for performance improvement of single-channel ECG based sleep staging in 4-class(W-L-D-R) and 3-class(W-N-R) classification.