The police are investigating the treatment suffered by Campbell, whose move from Tottenham to Arsenal still rankles with some Spurs fans, while the FA have launched their own investigation.
Triesman continued: "I abhor the treatment dished out to Sol Campbell by Spurs fans, and I hope that the individuals can be identified and banned from the Tottenham ground.
"Those fans have let themselves down and their club down in a way that is just unacceptable. We have to be very clear about it.
"People tell me that it is very hard to drive out these kind of things, but people said that about racism during the days when you heard racist chanting at virtually every ground.
"It was possible to do a great deal about that, although not enough yet. It is a matter of obligation. It is up to the clubs not to have the supporters in the ground who chant that kind of abuse."
