The leader of Labour's campaign to remain in the EU has told BBC Wales it was "unfair" to think European economic aid money would solve the problems of the poorest parts of the country.
Alan Johnson said Wales still needed to work towards its own destiny.
The EU is providing £1.8bn to Wales between 2014 and 2020, to spend on schemes to improve economic growth.
But some campaigners to leave said some money saved by not paying EU membership fees could be spent on the poor areas.
Between 2000 and 2006, Wales was awarded more than £1.5bn of European funding.
In the second round of funding, between 2007 and 2013, programmes for west Wales and the valleys – covering 15 local authority areas – invested £1.8bn in funds.
When the first round of funding was announced in 2000, the then-First Minister Rhodri Morgan said: "We now have a once-in-a-generation opportunity to transform our economy and make a major difference to the lives of people in west Wales and the valleys."
But there have been criticisms of the way the money has been used, since areas supposed to have benefited remain among the poorest in the EU.
On a visit to a project in Cardiff University, funded in part by the EU, Mr Johnson said it was not realistic to have thought EU funding would create "a land of milk and honey".
He told BBC Wales Sunday Politics programme: "Europe isn't going to solve all our problems. Europe isn't going to take away the necessity for us to work towards our own destiny, whether that's at Westminster or Cardiff.
"Yes, Europe has this ambition that all parts of Europe should come up to the same level of prosperity, and you've seen that money come to you in Wales, but to somehow grudgingly say 'ah, but it hasn't created a land of milk and honey', I think is a bit unfair."
A spokesman for Grassroots, a cross-party campaign to leave the EU, said money saved on membership fees "would be better spent on schools and hospitals in Wales and in the poorest parts of our own communities".
"Welsh taxpayers' money should be spent in Wales, not given to other countries in the European Union," he said.
Last week, David Cameron told BBC Wales voters "could not be certain" that the UK government would spend the same amounts if the UK left the EU.
Sunday Politics is on BBC One Wales at 11:00 GMT