In this paper, an adaptive pilot assignment scheme is proposed to solve pilot contamination (PC) caused by the reuse of limited pilot sequences, while allowing massive access in the scalable Cell-free massive multiple-input multiple-output systems. The proposed allocation scheme consists of algorithms for determining initial serving relationships between access points (APs) and user equipments (UEs), and an adaptive group forming strategy where groups are formed with UEs that contain the least common associated APs. The proposed scheme guarantees the association of all UEs and better spectral efficiency (SE) by reducing PC efficiently with limited pilot sequences. Numerical results prove that the proposed allocation scheme outperforms the random assignment scheme and a recent pilot assignment proposal that allows massive access in respect to 95%-likely SE and average SE performance.