We investigate the influence of metamaterials on the scaling laws of the transmission on multilayered structures composed of random sequences of ordinary dielectric and metamaterial layers. The spectrally averaged transmission in a frequency range around the fully transparent resonant mode is shown to decay with the total number of layers as 1/N. Such thickness dependence is faster than the 1/N(1/2) decay recently reported to take place in random sequences of ordinary dielectric slabs. The interplay of strong localization and the emergence of resonant modes within the gap leads to a non-monotonous disorder dependence of the transmission that reaches a minimum at an intermediate disorder strength.