Clinton squandered that opportunity when he bombed Serbia. It gave the Russian hardliners fodder to point out that the US was still going to try to contain Russia.
That was the war that baffled me. I will admit that there is a peace in the region I never saw coming prior to our actions, but the bombing we conducted was just plain idiotic to my way of thinking.
I could be wrong here.
In truth, I never viewed it as anti-Russia. Russia may have seen it differently though, more close to your view.