I think clearly there have been a series of actions that NATO has undertaken over the years, from Kosovo onward, that the Russians have taken great exception to.
There are two angles here. The first is NATO taking action that the Russians are uncomfortable with because of the action itself; the second is that it demonstrates quite clearly NATO's capacity to intervene in regions outside of its own area of operations, which reinforces the Russian fear that NATO, as perceived within Russia, is a tool of western hegemony.
They didn't oppose the intervention actively in Libya, but they were very uncomfortable with it and felt taken along, as if on a train. They felt they faced undesirable choices one way or the other.
Again, I emphasize that this is a Russian perspective; it's not necessarily my perspective, but I'm often explaining perspectives that are different from our own.
From their perspective, this underlines their relative weakness with regard to the alliance, and their own need, therefore, to maintain vigilance to not trust the alliance. They perceive the willingness of the Americans and the alliance as a whole to move forward on projects such as missile defence and the development of novel conventional capabilities, whatever the consequence on the perceived security of other states, as indicators that NATO is not to be trusted.