First-pass perfusion cardiac magnetic resonance (FPP-CMR) is becoming essential to detect blow flow anomalies. However, the need for real-time acquisitions limits the achievable spatial resolution and coverage of the heart. To keep both within a reasonable range, FPP-CMR needs to be accelerated. A SElf-Supervised aCcelerated REconsTruction (SECRET) DL framework is presented to speed-up reconstruction of FPP-CMR images from undersampled (k,t)-space data. The physical reconstruction models are used to train deep neural networks without requiring fully sampled images. SECRET achieves good quality reconstructions at a variety of acceleration rates, with significant speed-ups compared to the state-of-the-art.