The Welsh secretary said Labour had let down west Wales and the valleys.
Speaking at the Conservative Party conference in Birmingham, Mr Cairns said some areas, which had the most EU funds, voted more heavily to leave.
A spokesman for First Minister Carwyn Jones insisted EU-funded programmes had made a "big difference" in Wales.
Mr Cairns accused Mr Jones of trying to present Wales as "a victim of the EU referendum", following the majority vote across the UK for Brexit.
"He seems to forget that Wales voted to leave the European Union too," he said.
Mr Cairns argued Brexit represented an opportunity to do things better - and warned "carrying on in the same old way, spending according to the same old plans after two decades is not an option any longer".
"After all, European structural funds are supposed to be a temporary fix, a stimulus for the most deprived parts of the UK.
"In Wales in 1999 I remember the debate about Objective One money - it was described as a 'once-in-a-generation opportunity'.
"But 16 years on, £4bn later, Labour's mismanagement of the funds has let those communities down.
"So much was their frustration that those areas that had received most European aid were the very same areas that voted in the strongest numbers to leave the European Union.
"If only they [Labour] had focused on the outcomes in the same way that they focused on the money that they were spending in those projects."
Mr Cairns told the conference the new structure after Brexit "will give us the opportunity to follow UK priorities, investing in a way that is completely tailored to the Welsh and the UK economy".
The Vale of Glamorgan MP singled out Mr Jones for criticism, but added: "Whether we like it or not, we must work from that instruction.
"There are new and exciting opportunities for Wales with the UK being the global leader in free trade."
Mr Cairns argued the new Department for International Trade will be "fundamental" to seek out new markets and increase inward investment for Wales.
A spokesman for the first minister said there was an "astonishing paradox" in Mr Cairns's remarks.
"First he celebrates the good employment figures in Wales, and then he trashes European funding," he said.
"The truth is that European funded programmes, like Jobs Growth Wales, have made a big difference to Welsh businesses and job-seekers.
"The reason Wales is out-stripping other parts of the UK doesn't have anything to do with the Tories in Westminster."
Alun Cairns has launched a fierce attack on the "mismanagement" of £4bn of EU grants by the Welsh Government intended to help the poorest areas.