The EU must learn a lesson on how it informs people about money being spent to help poorer areas, the commissioner responsible for the regions has said.
Corina Cretu said she respected Wales' vote for Brexit, but called it unfortunate and regrettable.
West Wales and the Valleys have received almost £4bn since 2002 and recently qualified for more funding.
The aim is to create jobs and increase wealth and prosperity to bring the region closer to the EU average.
"There were some regions in transition which have received a lot of money and we were there as a sign of solidarity in many moments of crisis for some regions, for instance when the mines were closed," said Ms Cretu, a former Romanian MEP who has been EU commissioner for regional policy since 2014.
"We have trained people; we have opened, due to European funds, many new activities.
"But of course this speaks also about our weaknesses of communicating what we are doing with European money, how European money is spent, so it's a lesson for us."
She said communication of EU funding for Wales had not been effective before the Brexit vote.
Leader of the Welsh Conservatives, Andrew RT Davies, who campaigned to leave the EU, said: "Clearly they've learnt nothing at all from the referendum campaign, or the result.
"The problem isn't public relations, it's outcomes - and Wales' poorest communities have been repeatedly let down over many years; not by a failure to communicate, but by a failure to make meaningful improvements to people's lives."
WHAT DO WE WANT FROM BREXIT? MONTY'S BREWERY, MONTGOMERY, POWYS
Russ Honeyman is co-owner of Monty's brewery in Montgomery, Powys, which has been going since 2009. His wife Pam is head brewer.
They are looking to increase their exports - which accounts for about 5% of business.
Mr Honeyman voted to leave and believes the UK government has a difficult balancing act.
"I want to trade with Europe which is relatively easy at the moment. But there's the other side with migration and other issues so I can understand why it's taken time to make these decisions," he said.
"Everybody wants something different out of it. We want to be able to trade with Europe and buy stuff in. Some of the kegs we use for export we buy in from Belgium and Holland. We also want to be able to sell back.
"We're also looking to sell in Australia and have some interest from America - so it doesn't necessarily have to be EU trade."
WHAT DO WE WANT FROM BREXIT? REAL PET FOOD COMPANY, FLINT, FLINTSHIRE
Graham Wheeler is managing director of the Real Pet Food Company, which started in 1999 as a start-up firm making specialist treats for dogs and cats.
It moved to Flint eight years ago and is now part of the IPN group. A new £6m factory is being built, with the hope of expanding the workforce from 30 to 50. Currently, 15% of its turnover is with the EU.
"Ideally we'd like to maintain as free a trade as possible," said Mr Wheeler. "We realise that's going to be tricky to achieve but that's what we need to maintain a competitive position in Europe and maintain our position there."
The firm would also like some free movement - as it finds it needs to supplement its recruitment with a proportion of migrant workers.
As for red tape, he said: "Legislation and regulations we're under [in the EU] are there for a good reason and I can't see they'd agree to dropping them for us if we're exporting into Europe because that would give us a competitive advantage and it's all about being at a level playing field if you've got free trade, isn't it?"
During the referendum, supporters of leaving the EU said the money was the UK's anyway and a future Westminster government could replace any funds lost as a result of Brexit.
The UK is a net contributor to the EU while Wales is a net beneficiary.
Ms Cretu told journalists in Brussels some UK regions did not believe such funding would be replaced after Brexit.
Prime Minister Theresa May has indicated that she will trigger Article 50 early next year when negotiations on the future relationship between the EU and UK will begin.
Ms Cretu accepted many businesses relied on access to the single market.
But she reiterated the commission's view that it could only continue if the UK allowed the free movement of labour and other EU obligations.
"My personal view is that access to the European market comes with the obligation of the UK to respect all freedoms of European citizens," she said.