Rio Ferdinand, Jason Roberts and Anton Ferdinand were among a group of leading black players who did not wear the anti-racist campaign Kick it Out T-shirt ahead of Premier League matches at the weekend.
And yesterday Wales and Aberdeen keeper Jason Brown claimed black players might reluctantly be driven towards setting up a breakaway anti-racism group because they feel not enough is being done.
"This is a moment for cool heads, not hot ones," Robertson said, noting that he has been a long-time supporter of football anti-racism charities such as Show Racism the Red Card and Kick it Out.
They have done "extraordinary work in this area" over a long period.
Robertson said: "I think that, whatever the frustrations, by far the best way to advance this agenda is to get in behind those bodies and to help them carry this work on into the future.
"Footballers are individuals and they take their own decisions.
"I acknowledge and support the work that has been done by the anti-racism bodies, particularly Kick it Out, and I would urge everybody to get behind them so they can continue the work they have been doing to try and kick this out of the game.
"I absolutely understand why the temperature is raised and why they feel very strongly about it but I think it is important that we back Kick it Out and continue to make progress in the way that it has over the last 20 years."
It is now a year since the John Terry/Anton Ferdinand incident which has caused much damage to the game.
More recently there were ugly scenes at this month's Under-21 game saw Uefa bring charges against both the Football Associations of England and Serbia.
The Serbian FA has been charged with racist chanting by fans and both associations were charged over the behaviour of their players.
England defender Danny Rose said he was subjected to racist chants during the Euro 2013 play-off match in Krusevac, which England won 1-0 for a 2-0 aggregate victory.
Rose was sent off after kicking the ball away at the end of the match and was pushed by Serbia players as he left the pitch, sparking a melee in which England staff jostled with members of the Serbia coaching team.
Robertson said: "I understand absolutely why feelings are running very high about this. It is clearly not just what is happening in this country.
"I could not believe it when I saw the video out take of the incident in Serbia.
"To think that sort of thing is still going on in this day and age is beyond belief."
One result of a summit at Downing Street was an extra £3 million being released for St George's Park, the Football Association's newly-opened National Football Centre in Staffordshire.
This money has been earmarked to encourage the development of black and minority ethnic coaches.
Robertson said: "It is in the hope that you can build up more people coaching at the grassroots so that will come through (to the top)."