The Communities Secretary, who has taken temporary charge of the response to the crisis, issued an unreserved apology to those affected in the Somerset Levels.
Repeated calls for dredging were made to Downing Street and other Whitehall departments by farmers and others in the region from at least six months ago but funding was declined.
“We made a mistake, there’s no doubt about that and we perhaps relied too much on the Environment Agency’s advice,” Mr Pickles told BBC1’s Andrew Marr Show.
“We recognise that we should have dredged and I think it is important now that we get on the process of getting those people back into their houses once we are able to really do some serious pumping.”
Mr Pickles has criticised under-fire EA chairman Lord Smith for refusing to say sorry for the failures when he was besieged by angry locals on a visit to Somerset.
Asked if Prime Minister David Cameron should also apologise, Mr Pickles said: “I’ll apologise. I’ll apologise unreservedly.”
The EA has faced fresh anger after a senior official hailed its performance as a “success story”.
Director of operations David Jordan told a press briefing that the 5,000 homes flooded during the winter storms were “individual tragedies”.
“But also we need to recognise that 1.3 million other properties would have flooded if these flood defences had not been built,” he said.
“That is the success story, if you like, that we are talking about.”
Mr Pickles – who has taken the lead while Environment Secretary Owen Paterson recovers from eye surgery – said the agency needed to revisit its priorities.
As politicians trade blows on the political fall-out from the disaster, police were investigating whether seven-year-old Zane Gbangbola, who died after falling ill in his flood-hit home in Chertsey, Surrey, may have become a victim of the floods.
Officers have refused to be drawn on whether carbon monoxide poisoning from a generator pumping out flood water from his home may have been to blame, which also saw his parents, Kye Gbangbola and Nicole Lawler, taken ill.
While tributes have been paid to the boy, two severe flood warnings remain place in the crisis-hit Somerset Levels – where villages are cut off and many residents have already been forced from their homes after weeks of heavy rain.
The Prince of Wales, the Prime Minister and Environment Secretary have all visited the Levels in recent weeks and the latest politician to visit was Ukip leader Nigel Farage.
During a visit to Burrowbridge, Mr Farage called for a public inquiry and reiterated calls for the Government to compensate victims.
“In the short term I want the Government to say they are going to compensate flood victims. Longer term there has got to be a public inquiry in how we are managing our rivers,” he said.
“There are times when a Government really needs to do something to support its own people. I just want to get this ball rolling.”
Mr Farage denied his visit was “political opportunism”.
“Unlike everybody else who turns up for a photo op and goes away again I am actually going to visit some of these properties, meet some of these people and get a better understanding,” he insisted.
“From what I can see, the Environment Agency appear to be so hamstrung by a whole series of European directives and we are putting the interests of beetles and voles and birdlife before that of farmers and people.”
Mr Farage also took the time to chat to locals and volunteers over a pint of ale in the King Alfred pub, which sits next to the River Parrett in Burrowbridge.
He was heckled by resident Mike Jay, who shouted at the politician “Oy Nigel, what are you going to do for us, rather than just a photo op?”
Mr Farage, who went up to Mr Jay to speak to him, replied: “I am trying to get off the ground a campaign that anyone who has suffered financial loss as a result of flooding actually gets compensation.
“I tell you why, because when we had the storm before Christmas I had a cracked chimney, roofing tiles gone, fencing down and the insurance company paid most of mine and I am £3,000 short.
“I’ve got a good salary and I can pay for it but people on fixed incomes and everything else can’t.”
Mr Cameron is to chair the latest meeting of the Government’s emergency Cobra committee this afternoon as forecasters warn of another week of storms.
Heavy rain and winds of more than 60mph will die down throughout today but the brief respite will be broken by another storm arriving tomorrow night.
There are nearly 300 low-level flood alerts and almost 200 medium-risk warnings in place across Wales and central and southern England.
The Met Office warned that river levels are expected to continue rising along the Thames, the Severn and the Dorset Stour this week.
The Ministry of Defence has put 1,600 personnel on six hours’ notice to help in the south.
Rail operators are now able to run trains to Exeter but there is still major disruption to services following flooding, landslides and collapsing track beds in the West Country.
In Croydon, South London, a pedestrian underpass has been turned into an emergency pond to hold hundreds of thousands of litres of floodwater threatening homes and businesses.
And reserve soldiers of 7 Battalion The Rifles were called in to use sandbags to dam a breach in the Kennet Canal which threatened an electrical sub-station near Burghfield, south of Reading.
Meanwhile, Met Office chief scientist Dame Julia Slingo said while there was not yet “definitive proof”, “all the evidence” pointed to a role for climate change in extreme weather.
She also delivered a grim warning that the country should prepare itself for more similar events in future.
It is the strongest link yet made by the Met Office between the intense weather and climate change, and backs David Cameron’s remark last month that he “very much suspects” a connection.
Labour former environment secretary Hilary Benn said “real progress” had been made after the Pitt Review into the summer floods of 2007, although added lessons could always will be learnt when dealing with “nature’s raw power”.
Green Party leader Natalie Bennett insisted Mr Paterson should be replaced as Environment Secretary.
She also said the Government and the previous Labour administration had not spent enough money on flood defences and the coalition’s cuts to the Environment Agency should be reversed.