The Standard Eurobarometer survey revealed half of Europeans also do not think that their voices count in the EU.
Immigration was the top concern, followed by the threat of terrorism. And most are against the key policy of future enlargement of the EU to include other countries.
The European Commission survey, carried out in November, showed that one in five people (21 per cent) had a negative image of the EU, 37 per cent were neutral and 40 per cent were positive.
Some 50 per cent disagreed that their “voice counts in the EU”, six per cent above those that did.
Concerns about immigration grew for the first time since autumn 2015, with 39 per cent, ranking it as the most important issue in the bloc.
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Terrorism rated 38 per cent.
The two issues were mentioned more than twice as often as any other, including the economic situation and crime.
Only a minority (42 per cent) backed further enlargement of the EU, 47 per cent opposed it.
Distrust in the EU rose slightly since the spring, with 48 per cent saying they “tend not to trust” the institution.
Only 41 per cent said they trusted it.