Vern Cotter is set to for his last game in charge before Gregor Townsend takes over in the summer,
Cotter, who is heading to Montpellier, has made vast improvements to the Scotland team but the Scottish RFU were desperate to keep Townsend in the country.
The decision was harsh on New Zealander Cotter, who will be joined at his new club by Alex King, who is currently helping Wales.
Russell, who is pressing for a place on this summer’s Lions tour, told the BBC: “Clearly we want to send him [Cotter] off on a high with a good display and a win, but for the players on the field, we have to do it for ourselves first and foremost.
"We can’t think, ‘We must do well for Vern’. We can’t be distracted from what we need to do on the field. If we can stick to our game-plan, then the result will take care of itself.
“Italy have lost every game in the championship but I think that only tells part of the story. They have definitely improved under Conor O’Shea and Ireland are the only team to really dominate them so far.”