In this article, the adaptive event-triggered containment control problem is investigated for a class of uncertain nonlinear multi-agent systems with an adjustable funnel function. To address the high-frequency oscillations or overshooting problem of fast learning, a predictor is considered. Different from the existing event-triggered control results, a novel adaptive event-triggered condition is designed, which depends on the prediction error instead of relative state error. In order to further improve both the transient and steady-state performance, a modified funnel control strategy is introduced, and distributed containment errors are converged to an adjustable funnel boundary. The proposed control scheme guarantees that the closed-loop system is stable and all followers converge to the convex hull constructed by the leaders. Finally, two simulation examples are provided to confirm the effectiveness of the proposed control method.