Cameron said Britain should be proud of the achievements of the campaign to rid the sport of racism over the past two decades, adding that other countries had failed to take similar action.
"But we have some problems still today," Cameron said at the opening of an anti-discrimination summit with former players and football officials. "We need to act quickly to make sure those problems do not creep back in.
"If everyone plays their role, then we can easily crush and deal with this problem.
"We want to make sure football is all about a power to do good, rather than anything else."
"What happens on the field influences what happens off the field. You see children as young as six imitating the behaviour they see on the field," he told a panel including former England internationals John Barnes and Graeme Le Saux.
"So this is not just important for football, it's important for the whole country."
Earlier this month, Liverpool's Uruguayan striker Luis Suarez was forced to apologise for refusing to shake hands with Manchester United's French defender Patrice Evra before a Premier League match.
