Jon Moulton, founder of City Link's parent company, has denied the firm's collapse was mishandled.
News of City Link's failure was announced on Christmas Eve, but he said the timing could not have been avoided and has apologised to staff.
However, the timing and manner of the announcement has been criticised, with two Tory MP saying it was "appalling".
Meanwhile, the administrators running City Link have warned of "substantial" jobs cuts among the 2,727 staff.
Mr Moulton, founder of investment business Better Capital, told Radio 4's Today programme: "We chased every possible way to save this company."
He said that delaying the closure of City Link over Christmas had not been an option, as trading while insolvent was a criminal offence.
"We're very sorry about the failure of City Link and we're very sorry about the horrible effects that will follow for the workforce and contractors," Mr Moulton said. "I'm afraid that is the result of the company failing, nothing more nothing less."
He also defended criticism that taxpayers would end up paying for City Link staff's redundancy following administrator Ernst & Young's (EY) statement that it would refer employees to the government's statutory redundancy payments scheme.
Transport Union RMT's General Secretary Mick Cash said: "It says everything about the state of industry in Britain today that a donor to the party of government can wreck the lives of thousands of people, walk away and leave the taxpayer to pick up the redundancy costs."
But Mr Moulton said: "I don't think the taxpayer is going to end up footing much of a bill on this." He said that City Link had paid "a fortune" in taxes such as PAYE and said ultimately the government would be a net beneficiary of Better Capital's investment in the firm.
"The taxpayer has certainly made an enormous amount of money out of private equity companies and their trading and success.
"We are looking after money that has been given to us to invest, we are in the business of trying to make money for our investors," he added.
Mr Moulton, a multi-millionaire, said he personally had lost £2m on the firm's investment in City Link.
However, concern about the way the collapse was handled has been growing. Two Tory MPs, former minister Damian Green and backbencher Tracey Crouch, are calling for "urgent discussions" with ministers.
Both MPs have City Link depots in their Kent constituencies.
Mr Green said: "The whole business has been handled very badly, and I will be trying to ensure something is salvaged, for the sake of the employees."
Tracey Crouch said: "The manner in which employees have been treated in this process is utterly appalling. The least they deserve now is the best possible redundancy terms and support from the Government where possible."
The shadow business secretary, Chuka Umunna, said that ministers and the government should use their influence to intervene.
He has written to Mr Cable to ask "when BIS was first made aware of the situation facing City Link and what action was taken to prepare for the possibility of the firm going into administration".
Meanwhile, in a statement on Monday, Ernst & Young said it had begun telling staff to expect heavy job cuts.
"While no redundancies have been made today, the joint administrators believe that the company will unfortunately have to make substantial redundancies, which will take effect on 31 December.
"Employees that are not immediately affected by redundancies will continue to be employed, and paid, to help return the estimated 40,000 parcels remaining in City Link's depots to customers and intended recipients, as well as assist in realising the company's assets and winding down its operations," the company said.
The firm has said that parcel depots would "remain open for a short period of time" to enable customers and intended recipients to collect their parcels.
There are still about 40,000 parcels at City Link depots across the country, E&Y said.
It advised customers to use City Link's online tracking system to find out which depot to go to.
Coventry-based City Link, founded in 1969 and was acquired by restructuring specialist Better Capital for just £1 in April 2013, called in administrators on Christmas Eve after years of "substantial losses".
The administrators said on Friday that they were gathering expressions of interest from parties interested in acquiring specific assets, divisions of the business or the entire firm, it added.
But E&Y added that given the previous unsuccessful sale process administrators were "cautious about the prospects of finding a buyer".