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 Agency chairman Lord Smith for refusing to say sorry for the failures when he was besieged by angry locals on visit to the area.
Asked if Prime Minister David Cameron should also apologise, Mr Pickles said: “I’ll apologise. I’ll apologise unreservedly.
“I am really sorry that we took the advice ... we thought we were dealing with experts.”
The Agency was “fit for purpose” and its staff were doing a fantastic job on the ground dealing with the floods but there were serious questions about parts of its leadership, he said.
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.
And more storms will continue to batter Britain until the weekend, weather forecasters MeteoGroup predicted.
The Environment Agency 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.
“That is the success story, if you like, that we are talking about.”
Mr Pickles said: “Of course it is fit for purpose. It may have made some misjudgements but right now the men and women of the Environment Agency are working around the clock doing some fantastic jobs shoring up our flood defences and are offering advice.”
He once again declined to give his backing to Labour peer Lord Smith, who faces calls to quit ahead of the end of his present term in July.
“I don’t see myself becoming the advocate of the ‘Save Chris Smith’ campaign or printing ‘Save The Environment Agency One’ T-shirts,” he told the Mail on Sunday.
The Agency had “become riddled with political correctness” which had led it to halt vital drainage work such as dredging the Parrett and Tone rivers to take water away from the Levels.
It worries me that in a politically correct attempt to be more environmentally sound than the next person, something as basic as this has been forgotten,” he said.
Mr Pickles - who has taken the lead while Environment Secretary Owen Paterson recovers from eye surgery - said the Agency needed to revisit its priorities.
It was the biggest such agency in Europe - and bigger than the American version, he pointed out.
“Roughly half its budget goes on staffing and I think they only spent about £20 million on cleaning culverts and the like. I’m sure now they’ll be reassessing.”
Asked if Lord Smith should fall on his sword, he told the Andrew Marr Show: “That’s a matter for him. I don’t think I should nudge him out.”
Two severe flood warnings remain place in the crisis-hit Somerset Levels - where many residents have already been forced from their homes after weeks of heavy rain.
There are around 270 low-level flood alerts and 179 medium-risk warnings in place across Wales and central and southern England.
After a brief respite, storms will continue to batter Britain until the weekend, weather forecasters MeteoGroup predicted.
The Met Office warned that river levels are expected to continue rising along the Thames, the Severn and the Dorset Stour this week.
Mr Pickles said the authorities were braced for “significant flooding” in the Thames Valley by the middle of the week as the slow-rising river bursts its banks in places.
The Ministry of Defence has put 1,600 personnel on six hours’ notice to help in the south.
He said the Government was working to get rail links to the South West “as quickly as possible” and had helped secure more and bigger-capacity flights to the region.
The West Country is now completely cut off by rail and operators have put on replacement bus services and slashed ticket prices for passengers.
Flooding at Athelney and between Taunton and Bridgwater in Somerset means that all mainline routes to the region from London are closed.
The diversionary route via Yeovil is also closed at Crewkerne because of a landslip and is expected to remain shut for up to a week.
This latest blow comes days after a stretch of the rail line connecting Cornwall to the rest of the country fell into the sea at Dawlish in Devon when an 80-yard stretch of the sea wall was destroyed by high tides and stormy seas.
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.
Mr Pickles took a cautious line on the influence of climate change on the extreme weather.
Met Office chief scientist Dame Julia Slingo said while there was not yet “definitive proof”, “all the evidence” pointed to a role for the phenomenon.
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.
But Mr Pickles said: “I’ve had the opportunity of listening to experts and after a little while it became pretty clear to me that from a really educated point of view nobody really knows.
“To a degree I don’t think it matters whether it’s climate change or whether it’s part of the cycle we normally see in weather - we’ve got to deal with the consequences.”
Ukip leader Nigel Farage has called for a public inquiry into the flooding that has devastated the Somerset Levels and said that the Government should compensate victims.
During a visit to flood-hit Burrowbridge, near Bridgwater, Mr Farage said he had been invited by two local party members to see for himself the problems residents were facing.
“I want to get a better understanding of the problems on the Somerset Levels and I also want to say that people here who are suffering, they will suffer not just emotional distress but severe financial loss because insurance companies never pay out 100%,” Mr Farage said.
“I just want Government to say ‘we’re going to support these people, the farmers, the householders in this area and we will compensate them for their loss’.
“My suggestion a couple of days ago was that we can use a small fraction of the foreign aid budget to look after these flood victims.
“Since I said that on Thursday Labour politicians, Conservative politicians, a national newspaper and the Sikh volunteers who are here, all support me.
“There are times when a Government really needs to do something to support its own people.
“This particular campaign to compensate individuals for financial loss is something I have started. I just want to get this ball rolling.”