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The leader‐following consensus problem of a class of non‐strict feedback multi‐agent systems with unknown disturbances, this paper develops a novel adaptive event‐triggered control strategy ground on the consideration of the full state constraints. Combining the dynamic surface control and event triggering mechanism, the unknown external disturbances are estimated by designing a disturbance observer. In order to deal with unknown functions, this paper employs the neural networks. On purpose of keeping the output variable within a constraint boundary, the barrier Lyapunov function is chosen during the design course. Then, through the backstepping method and the Lyapunov stability theorem, it is proved that all signals in the closed‐loop systems are bounded, and the control performance of the closed‐loop system is ensured by selecting design parameters reasonably. Eventually, the availability of the control strategy is guaranteed through experimental example. [ABSTRACT FROM AUTHOR]