The research found that pupils' experiences varied and often depended on their teachers' commitment to multicultural or anti-racist approaches.
Its publication coincided with a new report by HM Inspectorate of Education on race equality, giving examples of good practice in schools that created a culture of inclusion and equality.
The research study, Minority Ethnic Pupils' Experiences of School in Scotland (MEPESS), led by Rowena Arshad of the Centre for Education for Racial Equality in Scotland (CERES), concluded: "Teachers and parents in particular stressed that it was time race equality was recognised as relevant to people of all ethnicities rather than being exclusive to multi-ethnic schools.
"Teachers who were more experienced in race equality matters cautioned against the dilution of anti-racist discourse within the terminologies of 'generic inclusion and diversity'."
The group's research also found that minority ethnic parents saw schools as "failing to consider what avenues of involvement are genuinely open to those parents whose voices are not generally heard".
It added: "While the experience of racism on a regular basis was acknowledged by many minority ethnic pupils and parents, teachers tended to pride themselves on the school's success in dealing with racism.
"Consideration therefore needs to be given not just to putting in place effective reporting and recording mechanisms but also to the establishment of procedures which monitor how conflicts are resolved, particularly from the perspective of those individuals or groups which have been targeted."
The authors, however, issued an addendum to their report, saying that there had been a number of positive changes in the intervening three years. These included action by education authorities to comply with new race relations legislation. Curriculum and impact assessment had also improved.
The report none the less suggested that much remains to be done. "Careful monitoring is required to ensure that staff and pupils are adequately supported to take forward race equality work, and that all pupils are able to access effective education that prepares them for life and work in a diverse and multicultural society.
Areas requiring attention include staff development and "mainstreaming race equality" so it is seen as relevant for everybody; the attainment of minority ethnic pupils; and increasing the ethnic diversity of the workforce.
The report also calls for improvements in dealing with racist incidents, an embedding of race equality in the curriculum and more sharing of good practice.
Peter Peacock, Education Minister, said it was crucial for young people to understand and value many cultures, races and backgrounds. "There is already excellent work being done in schools across the country," Mr Peacock said, "and we are making real progress and plan to make more through the various initiatives we are funding."
A spokesman for the Executive pointed to initiatives such as an anti-bullying school competition on the theme of discrimination and the "One Scotland, Many Cultures" campaign.
He also underlined the importance of the new Standard for Full Registration. This expects that new teachers develop professional qualities and capabilities by the end of their probationary year, and includes awareness of issues that relate to race equality.