I was reading this article of the Guardian, which nuances this a little. It seems the young generations are more divided on the question, or at least regarding their support of Putin.
The Guardian view on Russian dissent: a slide to totalitarianism
(It is based on a recent poll, but which dates from a few days after the invasion, before the increase of sanctions.)
Even if they blame us, they perfectly know it's a consequence of Putin's actions, and the justification he gives may hopefully not be enough. I can't imagine how far their propaganda goes, they're infamous for it, but we see that the military themselves are realizing it's BS. It's not something that can be contained for a long time at this scale. Of course as @fadedc; said, there are severe repressive measures too ("
Accounts of schoolchildren and their parents detained in police cells after laying flowers at the Ukrainian embassy").
Either way, the public will have time to make their mind based on facts later.