We study the topology of the cosmic Large-Scale Structures (LSS) produced by Millennium simulations (Springel , V. et al., 2005, Nature 432, 629) by means of Minkowski Functionals (MF). MF provide global morphological and topological characteristics of arbitrary structures. Applied to the density field of dark matter structure they reflect changes during time evolution of LSS. We analyse the simulated dark matter density field smoothed by Gaussian filters with different radii (from r=1.25 Mpc up to r=10 Mpc) at different evolution time (from z=127 up to z=0). We demonstrate that Gaussian smoothing with a large radius (r=10 Mpc) do not properly reflect topological changes in the dark mater structure during the evolution process and destroys filamentary structure of the LSS at present Universe (z=0), which remains present in the density field smoothed by the filters with small radii (r=1.25 Mpc or r=2.5 Mpc). Transformation of the LSS from a nearly random distribution of matter at early stage of the Universe to the filamentary structure at present time corresponds to the onset and increase of an asymmetry in MF_2, MF_3 and MF_4 with respect to the mean density value.