But when asked if it was his last job in management, the 61-year-old said: "Who knows? We`ll wait and see."
Allardyce acknowledged it was a "silly thing to do" but was critical of the way his wrongdoing was uncovered.
The former Bolton, West Ham and Sunderland boss said: "Unfortunately it was an error of judgement on my behalf.
"I`ve paid the consequences. Entrapment has won on this occasion and I have to accept that."
Earlier, he told Sky Sports he had only attended the meeting with the undercover reporters as a favour to friend and agent Scott McGarvey, who he says was hoping to land a job out of it.
He added: "The agreement was done very amicably with The FA and I apologise to those and all concerned in the unfortunate position I`ve put myself in."
Allardyce was speaking to reporters outside his home on Wednesday before leaving the country to go on holiday.
He wished England Under-21s manager Gareth Southgate, who has been placed in temporary charge of the national side, and the rest of the players and staff "all the very best".
England`s next match is a 2018 World Cup qualifier against Malta on Saturday, 8 October.
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