MPs also said homophobia may now be the most prevalent form of discrimination.
The report responds to "continuing concerns" following the Patrice Evra-Luis Suarez and John Terry cases.
John Whittingdale MP, chair of the inquiry, said: "Recent incidents of racist abuse in the UK highlight that there remain significant problems."
Last December, Liverpool's Suarez was handed an eight-match ban and a £40,000 fine by the Football Association after being found guilty of racially abusing Manchester United's Evra.
In July, ex-England captain John Terry was cleared of racially abusing fellow footballer Anton Ferdinand.
Outside of English football, Euro 2012 was affected by instances of racist chanting at training sessions and matches. The Croatian Football Federation was fined 80,000 euros (£65,000) after fans directed racist abuse at Italy striker Mario Balotelli.
The Culture, Media and Sport committee report said that behaviour and the atmosphere at football matches had "changed hugely" since the 1970s and 80s "when racial and other forms of abuse were common".
It added that several initiatives and charities such as Show Racism the Red Card have helped to reduce racism where it is most prevalent - on the streets, in the grounds and online - but more still needs to be done.
"While the general level of progress in combating racism and racist abuse in the UK is positive, there is much more that can and must be done," added Whittingdale.
"We believe it is for the FA to take the lead and set the example for everyone, from football authorities at all levels to the grassroots groups, to follow."
In a joint statement, the FA, the Premier League and the Football League acknowledged the need to address discrimination in football.
- Relief as surgeons re-attach man’s severed private organ
- Can medical board really bite finger that feeds it?
- Mother claims nurse watched her newborn die
- Governor’s encounter with leaky roofs in school
- Police arrest former councillor for piracy
- Cord leaders allege ploy by State to ‘kill’ devolution through Ministry