Earlier this month, the American team decided to terminate Mazepin's contract for the coming F1 season, along with that of sponsor Uralkali owned by father Dmitry, as a result of Russia's highly condemned invasion of Ukraine.
The 23-year-old further added he had received messages of support from a number of other drivers, one of whom was Mercedes' Russell.
Asked about the nature of the comment, in particular given the sensitivity of the global situation at present, Russell said: "There was absolutely nothing political.
"I think all of our views, of what is going on in the world, are absolutely united.
"But obviously for Nikita, I've known him personally for a very long time. I was team-mates with him."
Speaking of a driver he partnered with at Hitech in the F3 European Championship in 2016, Russell added: "Obviously, regardless of his background, he is a driver who has dreamt of Formula 1 his whole career and reached it.
"Now that dream has disappeared for the obvious reasons.
"I just said 'Keep you chin up', as simple as that. Nothing political in it. Just personal."