Legged robots have the potential to show locomotion performance with reduced control effort and energy efficiency by leveraging elastic structures inspired by animals' elastic tendons and muscles. However, it remains a challenge to match the natural dynamics of complex legged robots and their control task dynamics. Here we present a framework to match control task dynamics and natural dynamics based on the neuroelasticity and neuroplasticity concept. Inspired by animals we design quadruped robot Morti with strong natural dynamics as a testing platform. It is controlled through a bioinspired closed-loop central pattern generator (CPG) that is designed to neuroelastically mitigate short term perturbations using sparse contact feedback. We use the amount of neuroelastic activity as a proxy to quantify the dynamics' mismatching. By minimizing neuroelastic activity, we neuroplastically match the control task dynamics to the robot's natural dynamics. Through matching the robot learns to walk within one hour with only sparse feedback and improves its energy efficiency without explicitly minimizing it in the cost function.