The 33-year-old is gearing up for his first season as part of Mark Warburton's Glasgow Rangers side.
The 33-year-old has stoked the fire ahead of the first Old Firm meeting in the Scottish Premiership for four years by suggesting that the Hoops midfielder is not in the same league as Barton.
And upon hearing the comments, Russell has suggested that the former Burnley man now has no choice but to ensure that his performances are of the highest quality.
"If he is talking like that before a ball is kicked, then he will know that he has to produce it on the park. Rangers supporters aren't daft and if he is not doing it on the park then they will not be slow in giving him a bit of stick," he told the Evening Times.
"He has got to back up his words with his performances. Scott Brown has got five titles in his locker and Joey will be determined to get his first in Scottish football."
Though Brown endured a largely disappointing campaign this past season, the 30-year-old's form could be predominantly put down to injury, and it must not be forgotten that he has still been a key player for a Bhoys side that has won six league titles, with the most recent five coming consecutively.
Therefore, for Barton to prove for his comments to be correct, he will need to replicate the kind of form that inspired the Clarets to the Championship title this past season.
The one-time England international appears to be the kind of player that would make such remarks about their bitter rivals' talisman - regardless of whether he actually believes them or not - to establish himself as his own side's key player and to motivate himself to find his best form to inspire the Light Blues back towards the top.