Among Russians over 30 years old, there is probably a common visceral sentiment that "we were the world's superpower until the United States dethroned us". Because Russia did not lose it's relative power in a conventional fight there is probably an undercurrent of hostility regarding the strategic thinking of American policymakers or of the imagined cleverness of American generally.

Russians do have concerns about Islamic extremists, but they are more likely than Americans to recognize that extremist Islam is a phenomenon marked by primitiveness rather than sophistication. Thus there are probably many influential Russians who overtly support the western fight against "Islamic terror" while discreetly operating to put America in an inferior position.

This is one of the most important considerations in the War on Terror.