Allardyce also remained coy as to whether he would get another job in football
Sam Allardyce claimed "entrapment has won on this occasion" following his resignation as England football manager after being caught in a newspaper sting.
The 61-year-old was forced to quit the post after he was filmed apparently trying to broker a £400,000 deal and telling businessmen how to evade strict rules on third-party ownership - a practice banned by FIFA since May 2015.
However, the 'businessmen' turned out to be undercover reporters carrying out a Daily Telegraph investigation.
A sombre-looking Allardyce, whose tenure as manager of the national football team lasted 67 days and just one match, emerged from his Bolton home this morning to face the media.
"On reflection, it was a silly thing to do... and I have paid the consequences," he said. "I am going to go away and reflect on it.
"I would like to wish all the England lads, Gareth and the staff, all the very best."
Asked if it was his last job in football, he replied: "Who knows?"
However, he contacted Sky Sports News earlier and insisted he was "not a quitter", that football was in his "veins" and he would "never quit" the sport, hinting at a possible return in the future.
He told Sky he was "very hurt and extremely disappointed" he was no longer the England boss and could not express in words how "sad" and "very down" he was to lose his job.
Allardyce said he was leaving the country for a break to reflect on what had happened, insisting he attended the hotel meeting as a favour to football agent Scott McGarvey, who he said was "down on his luck".
He said the pair had known each other for 20 to 30 years and he was "trying to help him out".
There were discussions about a public speaking contract for him, but Allardyce asserted his "main motivation was not money", but "to help an old friend".
He said he was "extremely sorry" and accepts he made "a huge error of judgement".
Allardyce, who was filmed on a hidden camera by undercover reporters, was asked about the rules on third-party ownership and is seen responding in the footage, saying: "It's not a problem.
He said an unnamed group had been "doing it for years" and "you can still get around it".
Allardyce saved Sunderland from relegation last season before he took over from Roy Hodgson, who quit after England's dismal showing in the Euro Championships this summer.
England Under-21 manager Gareth Southgate has agreed to step in as interim boss for the senior team's next four games, the first of which is against Malta on 8 October.
He is currently the bookies' favourite to keep the job on a permanent basis.
Allardyce met with FA bosses, including chairman Greg Clarke, on Tuesday to explain and apologise for the affair, when it was agreed he would leave the England job "by mutual agreement".