Fankhauser claimed his ability to save the company – a British institution founded 178 years ago – was hampered by a debt mountain built up in the years before he took charge.
Describing himself as "devastated", he said: "You ask me how I feel? Desperate. And deeply sorry."
He added: "I'm grateful for the loyalty of millions of customers. And I feel deeply, deeply sorry that they suffered this crisis. I can't say more than that. I can just tell them I tried everything for this company."
Thomas Cook fell into liquidation – ceasing all of its operations – at around 2am on Monday.
Since then 92,700 tourists have been flown home from 53 airports in 18 countries in the biggest ever peacetime repatriation of British citizens.
The mission, known as Operation Matterhorn, is being led by the Civil Aviation Authority. It aims to bring back more than 150,000 Thomas Cook customers by next Sunday.
The CAA said 95 per cent were flown home on the day they had been scheduled to return. Thousands of others are being refunded for Thomas Cook holidays that will now not take place.
The ruin of Thomas Cook – a travel industry giant with annual revenues of around £10 billion ($19b) – has also led to misery for thousands of employees, 9,000 of whom are based in Britain. More than 1,000 staff plan to take legal action after losing their jobs at short notice and missing out on pay.
Fankhauser, who like many of his former staff was not paid for his work in September, spent much of last week talking to his workforce, including at one of Thomas Cook's largest offices, in Peterborough.
He said: "It would not have been right not to go there. But it was tough. I talked to colleagues in small groups. They were crying. They were asking very, very difficult questions, 'How did it come to that? Couldn't you have made all the decisions better?' All the questions I ask myself as well, of course."
Fankhauser and the Thomas Cook board now face a parliamentary inquiry focusing on their pay after The Mail on Sunday revealed they had been paid more than £20m
($39m) over the past five years.
The revelation led to widespread condemnation, including from the PM. Later in the week, Parliament's Business Select Committee – led by Labour MP Rachel Reeves – started an inquiry into Thomas Cook's collapse. It will examine bosses' pay. Ms Reeves said the firm's demise appeared to have laid bare "a sorry tale of corporate greed".
But Fankhauser said he welcomed the inquiry, telling the Mail on Sunday: "I don't think that I'm the fat cat that I'm being described as."
Fankhauser accepted the blame for not securing a £200m deal with the Government that would have rescued Thomas Cook. But he added that, due to the company's large debt pile, he would have done nothing differently if he had his time again.
