Computational homogenization enables replacement of a heterogeneous domain by an equivalent body with effective material parameters. Approach that we use is based on two-scale micro/macro analysis. In the micro-scale heterogeneous properties are collected in so-called representative volume elements (RVE), which are small enough to satisfy separation scale condition, but also large enough to contain all information about material heterogeneity. In the macro-scale the material is assumed as a homogeneous with the effective material parameters obtained during RVE analysis. The coupling between both scales is provided at the selected macro-level points, which are associated to independent RVE. Then, approximation of solution in the whole domain is performed. Even though such a homogenization significantly reduces the time of computation, the efficiency and accuracy of the analysis are still not trivial issues. In the micro-level it is required to guarantee accurate representation of heterogeneity and at both scales the optimal number of degrees of freedom should be used. The paper presents application of one of the most efficient numerical techniques, i.e. automatic hp-adaptive FEM that enables a user to obtain error-controlled results in rather short time, assessment of homogenization error, that is crucial for determination of parts of the body, where homogenization cannot be used and the hp-mixed FEM discretization details.