There might be truth to what Putin says, but Putin is literally the last guy on earth to lecture US for doing that. Or maybe the second last, after Kim Jong-un.
Russian people are basically made to expect a war with the west anytime soon, as a result of government propaganda, and imagine that they live in a world where everyone is out to get Russia, and whatever Putin does is the very minimum self-defense against hostile Americans etc. It's a textbook case of blaming an outsider for internal problems.
The intensity of government propaganda is a bit different in an authoritarian state than anything done in the west, because of the state control of the media. For comparison, imagine Trump campaign blaming Mexicans for everything, the campaign would last for 15 years straight and was the only source of news in the US. That's how Russia is like.