The energy and rapidity dependence of the average transverse momentum $langle p_T rangle$ in $pp$ and $pA$ collisions at RHIC and LHC energies are estimated using the Colour Glass Condensate (CGC) formalism. We update previous predictions for the $p_T$ - spectra using the hybrid formalism of the CGC approach and two phenomenological models for the dipole - target scattering amplitude. We demonstrate that these models are able to describe the RHIC and LHC data for the hadron production in $pp$, $dAu$ and $pPb$ collisions at $p_T le 20$ GeV. Moreover, we present our predictions for $langle p_T rangle$ and demonstrate that the ratio $langle p_{T}(y)rangle / langle p_{T}(y = 0)rangle$ decreases with the rapidity and has a behaviour similar to that predicted by hydrodynamical calculations.