Cardiac magnetic resonance (CMR) imaging is widely used to characterize cardiac morphology and function. To accelerate CMR imaging, various methods have been proposed to recover high-quality spatiotemporal CMR images from highly undersampled k-t space data. However, current CMR reconstruction techniques either fail to achieve satisfactory image quality or are restricted by the scarcity of ground truth data, leading to limited applicability in clinical scenarios. In this work, we proposed MoCo-INR, a new unsupervised method that integrates implicit neural representations (INR) with the conventional motion-compensated (MoCo) framework. Using explicit motion modeling and the continuous prior of INRs, MoCo-INR can produce accurate cardiac motion decomposition and high-quality CMR reconstruction. Furthermore, we introduce a new INR network architecture tailored to the CMR problem, which significantly stabilizes model optimization. Experiments on retrospective (simulated) datasets demonstrate the superiority of MoCo-INR over state-of-the-art methods, achieving fast convergence and fine-detailed reconstructions at ultra-high acceleration factors (e.g., 20x in VISTA sampling). Additionally, evaluations on prospective (real-acquired) free-breathing CMR scans highlight the clinical practicality of MoCo-INR for real-time imaging. Several ablation studies further confirm the effectiveness of the critical components of MoCo-INR.