The ratios R_2k = g_2k/g^{k - 1}₄ of renormalized coupling constants g_2k entering the small-field equation of state approach universal values R∗_2k at criticality. They are calculated for the three-dimensional λψ⁴ field theory within the pseudo-ϵ expansion approach. Pseudo-ϵ expansions for R∗₆, R∗₈, R∗₁₀ are derived in the five-loop approximation, numerical estimates are obtained with a help of the Padé-Borel-Leroy resummation technique. Its use gives R∗₆ = 1.6488, the number which perfectly agrees with the most recent lattice result R∗₆ = 1.649. For the octic coupling the pseudo-ϵ expansion is less favorable numerically. Nevertheless the Padé-Borel-Leroy resummation leads to the estimate R∗₈ = 0.890 close to the values R∗₈ = 0.87, R∗₈ = 0.857 extracted from the lattice and field-theoretical calculations. The pseudo-ϵ expansion for R∗₁₀ turns out to have big and rapidly increasing coefficients. This makes correspondent estimates strongly dependent on the Borel-Leroy shift parameter b and prevents proper evaluation of R∗₁₀