The crusades, by and large, were a Catholic Christian thing. Only in the first crusade did the Orthodox Christians get involved. And it was actually at the request of the Byzantine Roman Emperor that the first crusade was launched. But the Roman Emperor didn't really get along well with the western (Frankish) crusaders, who basically ended their alliance as soon as they set up their own kingdoms in Outremer. Russia wasn't even a country at the time anyways. There were just random smatterings of city states, Novgorod in particular, as well as the Muscovites and Kievan Rus. They were far removed from the area and had their own problems to deal with.