This work introduces a new single-stage adaptive controller for Euler-Lagrange systems with nonholonomic constraints. The proposed mechanism provides a simpler design philosophy compared to double-stage mechanisms (that address kinematics and dynamics in two steps), while achieving analogous stability properties, i.e. stability of both original and internal states. Meanwhile, we do not require direct access to the internal states as required in state-of-the-art single-stage mechanisms. The proposed approach is studied via Lyapunov analysis, validated numerically on wheeled mobile robot dynamics and compared to a standard double-stage approach.@en