Its hard for HRC to deflect that to her boss. If she had stayed a senator or otherwise somehow not been involved, maybe the Russians wouldn't be so unhappy with her. She has been at the center of the last couple years of the USA/Russia trainwreck.
However its not totally impossible to deflect that to her boss. Her husband did "OK" with yelsin and met putin right at the end of his term. So she can likely argue its nothing personal or familial, its all an obama problem. And the Russians can turn right around and ask if she failed to advise her boss properly or failed to resign for ethical reasons, either way they have no reason to let her off the hook, unless she does something for them, maybe.
Trump being a businessman and a dealmaker and an outsider is almost certainly a better situation for Russia. He's stable and much more non-interventionist than Hillary. Its hard not to see how that would measurably benefit Russia (and, frankly, the USA)
More philosophically, lifetime politicians bend toward monopoly outlook, and american businessmen bend toward competition. A lifelong politician is going to inherently have an issue with the concept of a competing empire existing. A businessman isn't going to mind a competing land empire on the other side of the planet separated by a vast ocean full of our own navy. He's not going to be existentially scared of Russia. Scared people lash out, and that's dangerous with nuclear powers.
I'm not entirely sure I agree with the above arguments, but nobody else is bringing it up, so here it is.