At the meeting in the House of Commons, Mr Straw said much of the progress on race relations stemmed from the anti-racism work of inner-city education authorities 15 to 20 years ago.
He said: "They were really criticised for this. They were told it was political correctness. They were told they were being the thought police and all the rest of it.
"Now it is regarded as received wisdom. What we have got to do is make sure that it is rolled out in other areas, particularly white-only areas where we can get some serious racial stereotyping."
Mr Straw told the audience of young people that it was time to stop seeing race issues as a modern problem and start celebrating Britain's multi-cultural society.
"A hundred years ago there was in many ways worse discrimination, for example, against Jews and the Irish than there is today against black and Asian people," said Mr Straw.
"Many black and Asian people I speak to say what really cheeses them off is being regarded as a problem.
"What we have got to start doing is celebrating the fact that Britain has become a great society because it has always been a melting pot for people of different races and religions going right back to the Romans."
Facing questions from the audience, Mr Straw clashed with one student over whether he should have sacked Metropolitan Police Commissioner Sir Paul Condon after the inquiry report into the handling of the Stephen Lawrence murder investigation.
Mr Straw said the inquiry team had not called for his sacking. The commissioner had accepted there was institutional racism in the force and Sir Paul had put in place a programme "for securing change".
But Yasmine Amevor, 17, from Acland Burghley High School in Camden, London, said: "He should go and he should have gone already."