The minister told an audience of sixth-formers attending the launch of a new Foreign Office website that the results were "extraordinary". More than half of the 2,182 18 to 24-year-olds polled by ICM knew little or nothing about the EU.
The findings show teenagers are more Euro-stupid than Euro-sceptic despite the publicity surrounding the launch of the single currency. Many pupils will be handling the euro for the first time when they travel abroad this Easter.
Mr Hain said: "There are too many people in Britain, including a lot of young people, who do not really know about the EU. More should be done to teach pupils about Europe. That is not promoting any particular policy on Europe, but every school pupil is a European. It is vital that young people engage."
Camille Maison, a pupil at City of London school for girls, who attended the launch, said her interest in Europe had developed through general studies and politics AS-levels. But she said courses lower down the school should also have a European component.
Currently there are few opportunities in the national curriculum to study Europe. In history lessons, coverage of Britain since 1930 and key stage 3 world study after 1900 tend to be dominated by the Second World War. The United Nations and the Commonwealth are suggested as examples of topics, but not the EU.
Geography students are supposed to study different parts of the world including Europe. The interdependence of people and nations is also taught. The new citizenship curriculum, which will be compulsory from September, should improve students' EU knowledge.
Guidance from the Government's curriculum watchdog says schools should cover the role of the EU. However, there is a fear that teachers could avoid the topic, or boil it down to a dry explanation of the EU's institutions, because it is too political.
The guidance also gives advice on how to handle controversial issues. It says staff must decide how far they should express their own views, bearing in mind that they are in an influential position and must work within the school's values.