The counter-pulsation (CP) control of Pulsatile Extracorporeal Membrane Oxygenator(p-ECMO) contributes to reducing the risks associated with conventional ECMO, such as Left Ventricular dilatation and pulmonary edema. To achieve CP between p-ECMO and the heart, it is crucial to detect heartbeats and p-ECMO pulses in blood pressure (BP) waveform data, especially in cases where ECG measurement is challenging. This study aims to develop an algorithm utilizing deep neural network (DNN) to differentiate heartbeats from other pulses caused by p-ECMO, reflections, or motion artifacts in BP data, ensuring accurate CP control. A mock circulation system, replicating human BP waveforms with a heart model was connected to p-ECMO. Two trained DNNs were employed to measure the heart model's heart rate (HR) and evaluate whether p-ECMO operated in CP mode. In asynchronous mode experiments, the frequency of unintentionally occurring CP was only 25.75%. However, when utilizing the proposed algorithm, stable CP was observed, even when the initial pulse rate of p-ECMO differed from that of the heart model. Notably, even when the heart model changed its HR by 5 bpm every minute for 8 minutes within the range of 55 to 75 bpm, the CP success rate remained above 78%.