Nonlinear ultrasonic techniques have been developed over the last decades to detect the presence of damage in materials of interest in the field of civil engineering, such as concrete or mortar. The dependence on the strain amplitude of measurable quantities, such as wave velocity, damping factor, resonance frequency, etc. is normally considered a qualitative indicator of the presence of defects at the microstructural level. The experimental approaches proposed have the advantage of being sensitive to small variations in the sample microstructure and are therefore more adapted to detect the presence of small cracks or damaged areas with respect to traditional linear ultrasonic techniques. However, nonlinear methods are difficult to implement, since they usually require a calibrated experimental set-up which also behaves linearly at high amplitudes of excitation. The slow dynamics features, typical of the hysteresis generated by damage, have been given much less attention as a tool for damage detection even though their quantification is often less demanding in terms of an experimental set-up. Here, we provide the first evidence of how recovery, which is part of the slow dynamics process, is sensitive to the presence of damage in concrete samples and thus could be considered as an easy-to-measure nonlinear indicator for Structural Health Monitoring purposes.