Putin understands that a battlespace includes the minds of civilians just as much as it includes more obvious factors. The West, meanwhile, is largely crippled by relying on sensation-seeking journalists, who inevitably get nearly everything wrong and are always several steps behind reality. Thus Putin can control, to a degree not properly understood in the West, the narrative of the conflict.
Furthermore, Putin also understands human psychology. Ignorant foolish people love to feel "patriotic" during times of conflict and will rally round even the worst causes - just think of the US enthusiasm for the illegal, pointless, and stupid invasion of Iraq by the Baby Bush regime. So it's not really surprising that ordinary simple Russians prefer to believe the propaganda by which they are constantly bombarded each day.