The European Commission looked into whether the tech giants were meeting a pledge to remove hate speech within 24 hours of it being reported.
Only 40% of reports of hate speech are being removed within a day, it found.
The pledge was made in May when the firms signed up to a "code of conduct" brokered by the Commission.
"The last weeks and months have shown that social media companies need to live up to their important role and take up their share of responsibility when it comes to phenomena like online radicalisation, illegal hate speech or fake news," said Justice Commissioner Vera Jourova in a statement.
The research tracked what happened to 600 incidences of hate speech reported to the tech firms during a six-week period in October and November. The research covers that period because the monitoring system to track tech firms' responsiveness was set up in early October.
Campaign groups and NGOs that monitor racist and fascist movements across Europe used the notification systems on the different social media networks to report these incidences and then tracked how long it took the tech firms to act.
Of the 600 reports, 270 were made to Facebook, 163 to Twitter, 123 to YouTube and none to Microsoft. The remainder, seven reports, were made to social media groups that had not signed up to the May pledge.
The Commission said the 600 reports were a sample of racist, sexist and misogynist content and did not represent all the examples of hate speech on the tech firms' sites during the six-week study period.
About 20% of the messages seen were anti-Muslim and 23% were anti-semitic.
In 169 cases the content flagged as being hate speech was removed by the tech firms. YouTube removed 48.5% of the content reported to it, Facebook 28.3% and Twitter 19.1%.
In 40% of cases, reports were reviewed with 24 hours, found the research. In a further 43%, the reports were looked at within 48 hours.
"It is our duty to protect people in Europe from incitement to hatred and violence online," said Ms Jourova. "While IT Companies are moving in the right direction, the first results show that the IT companies will need to do more to make it a success."
Twitter, Facebook and YouTube are falling short of a commitment to tackle hate speech quickly, research suggests.