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."
MPs also said homophobia may now be the most prevalent form of discrimination.
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 British 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 needed to be done.
"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," said Whittingdale.
In a joint statement, the FA, the Premier League and the Football League said "substantial progress had been made", but acknowledged that "challenges remained" and said they would consider the committee's recommendations.
Steve Rotheram MP, a member of the Culture, Media and Sport committee, said a lack of ethnic diversity in management and boardroom positions at many English clubs was holding back the fight against racism.
He said: "Some boards are all-male and all-white with no diversity there, and managers in the top tier of the Premier League and the Championship are almost all white, so there are some glass ceilings that need to be broken down."
PFA chairman Clarke Carlisle added: "Now that this voice has come from outside of football and is one that hopefully the industry will listen to, it is very encouraging because it means things will have to progress from here."
When asked whether football needed to do more to tackle racism, Manchester United boss Sir Alex Ferguson said: "English football was very good at challenging those issues.
"Apart from last year, I don't think it's been an issue. I've not seen anything for 20 years. Suddenly, one bad year doesn't cast the game in doubt as far as I'm concerned."
The report also found evidence that homophobia may now be a bigger problem in football than other forms of discrimination.
As a result, it called for a high-profile campaign to highlight the damaging effect of homophobic language and behaviour at every level.
The report also called on football's governing bodies Fifa and Uefa to take stronger leadership on tackling racism.
SOURCE = BBC