The England full-back said that the campaign could be "cheapened" if it became the focus of a marketing exercise by Nike.
In a statement, the club said it supported anti-racism initiatives, including the campaign headed by Thierry Henry and supported by Neville's United team-mate Rio Ferdinand.
Nike has denied that it embarked on the campaign to gain free publicity and pointed out that the proceeds from anti-racism wristbands would be donated to charity. A spokesman said: "The campaign isn't about publicity, it's about racism. We've spoken with all the relevant bodies and we've had their approval."
There is understood to have been some friction between Arsenal and Manchester United players before the match on 1 February when Paul Scholes, Roy Keane and Gary Neville did not wear the "Stand Up - Speak Out" tracksuit tops that were designed for the occasion.
Neville said: "The FA and the England team have always campaigned against racism very well, we have just got to be aware that it is not cheapened by companies like Nike getting a lot of PR out of it for nothing."Reuse content