Ron and Penny Jones took Iraqi asylum seeker Ahmed Hassan into their home in Surrey, and said he "seemed like the loveliest boy we could have asked for".
But while the couple were on holiday in Blackpool, Hassan assembled the ingredients for homemade explosives in his bedroom in Sunbury, Surrey.
He used his student of the year award of a Â£20 Amazon voucher to buy one of the key chemicals online.
On Friday, he was convicted of attempted murder after the bomb partially exploded on the floor of a Tube carriage at Parsons Green in September last year, injuring 51 passengers.
In an interview with the Daily Mail, Mr and Mrs Jones said the authorities "should have been honest" with them, and spoke of their disbelief at how events unfolded.
"He still needed somewhere to live, he still needed to be looked after, but I would have liked to have known because we could've been looking out for signs of radicalisation," said Mrs Jones.
Mr Jones, 89, added: "If we'd known, we could have been more watchful. I still can't believe he did it. He seemed like such a good kid."
Hassan, who arrived in Britain on the back of a lorry in 2015, was referred by Barnardo's and Surrey social services to the anti-terrorism Prevent scheme, but kept his murderous plans a secret.
Mr Jones, who was awarded an MBE in 2010 along with his wife for services to fostering, told the Mail he had been "blaming myself but I've had nothing to be suspicious of".
Mrs Jones added: "I can only say he betrayed me. And out of the 269 kids we've had, he's the only one I can say that about."
A review of Hassan's dealings with Prevent is under way.
Security Minister and Wyre and North Preston MP, Ben Wallace, said there were "lessons to be learned", but also commended police, the CPS and security services.
He said: "This case is a bleak reminder of the devastating consequences of radicalisation."