The concept of local growth envelope of a quasi-normed function space is applied to the spaces of Besov and Triebel-Lizorkin type of generalized smoothness (s, Ψ) in the critical case s = n/p, where s stands for the main smoothness, Ψ is a perturbation and p stands for integrability. The expression obtained for the behaviour of the local growth envelope functions (which, as expected, depends on Ψ) shows the ability to be generalized to a form unifying both critical (s = n/p) and subcritical (s < n/p) cases.