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."

Police said the suspect was 26 years old and born in the United Arab Emirates. They said he acted alone and he was overpowered by passersby.
Mayor Olaf Scholz said the attack was motivated by "hate" but did not say it was a terror attack.
There are unconfirmed reports that the man shouted "Allahu akhbar", Arabic for "God is great" while attacking people.
Police said they were still seeking to confirm his current nationality. Mr Sholz said he was a failed asylum seeker.
The man attacked customers in the supermarket at random, ran outside and was chased by customers and by people outside the shop. They brought him to the ground before he was detained by plain-clothes police officers.
Mobile phone footage on German media that is purportedly of the attack's aftermath shows several people chasing a man and throwing chairs at him.
A 50-year-old woman and four men aged between 19 and 64 were stabbed, while a 35-year-old man was injured while helping overcome the suspect.
The attack happened in the Barmbek region in the north of the city in a branch of Edeka, Germany's largest supermarket chain.
Police say the man's weapon may have looked like a machete but they are, for now, assuming it was a kitchen knife.
One eyewitness made a gesture about 50cm (20 in) long when asked on German TV how big the knife was.
Asked whether this was a terror attack, a police official told the BBC: "We are at an early stage of the investigation... At the moment we can't rule anything out. We are investigating all avenues."
Speculation in German media said the attack may have been part of a robbery attempt but police said that that motive could not be confirmed.
One eyewitness, who ran from the scene into a nearby shop as the situation unfolded, told German broadcaster NTV that it seemed "hectic and confused, not like a properly planned attack".
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.
[NEXT_CONCEPT]
A 50-year-old German man has been killed and six people injured in a knife attack in a Hamburg supermarket.