Until the last moments, directors still believed a rescue was possible, but banks became more demanding, he said.
The details are included in a document Mr Cochrane has prepared as part of the insolvency process.
His statement sets out attempts to save Britain's second-biggest construction company after three profits warnings and a collapse in the share price.
Efforts to sell off parts of the business failed and Carillion's banks became more demanding, only agreeing fresh funding under tight new conditions that the company was unable to meet, the statement discloses.
There had been regular meetings with the government and its advisers in the final few months of 2017, Mr Cochrane says. But on 31 December a "formal request" was made for support from the government.
Even as late as last weekend, directors believed that "a constructive dialogue" was underway with banks and the government about providing short-term funding.
Directors wanted the government to "guarantee" more funding for four months while Carillion continued its restructuring, and be allowed to defer tax payments. Both requests were refused, according to Mr Cochrane.
But his document adds that "certain of the group's lenders took unilateral action which in the company's view undermined the group's efforts to conserve cash".
He singles out Royal Bank of Scotland (RBS) as one of the banks that wanted to impose tough new lending conditions.
RBS said in a statement that it had "provided considerable support and forbearance to Carillion over many months".
"The judgement of the bank was that the restructuring plan put forward by the company was not viable and therefore we took the difficult decision not to extend further funding and increase our exposure to the business."
Running out of cash and owing more than £1.3bn to its banks, Carillion declared itself insolvent on Monday.
Rather than attempt an orderly administration of Carillion in the hope of salvaging something from the business, the Official Receiver was appointed to liquidate the business.
Accountants EY and PwC both rejected requests to become administrators because there was no money left to keep the company ticking over, Mr Cochrane says.
Meanwhile, Treasury minister Liz Truss told the Commons on Tuesday that "it would be completely wrong for a public company that got itself in this state to be bailed out by the state".
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