Gareth Southgate replaced him as England manager and led them to the 2018 World Cup finals and Allardyce says he still struggles to get over his past.
"I think about it a lot. Especially when the England games come up and I've just been able to watch them again recently," Allardyce told Sky Sports.
"It was a really sad moment for me, having worked so hard to get to the pinnacle in my career - you're never going to get a job at a top club if you're English - so to get the England job is the pinnacle of your career.
"It is the greatest regret of my life in football. In terms of that disappointment, it will never leave me but there's nothing I can do about that now, I have to move on with my life."
Allardyce helped Premier League side Crystal Palace escape relegation last campaign before resigning in May and the former West Ham United manager has ruled out taking up Scotland's vacant managerial role.
The 62-year-old believes England, who last reached the World Cup quarter-finals in 2006, must maintain their fitness and overcome psychological barriers to succeed in Russia.
"There are already questions about what they will be like, but at some point, an England team will need to break that cycle, that negativity, by going further than expected," he added.
"If they are all fit at the end of the season, they could have a good tournament but they have to cope with the psychological side of it because that is the big drawback for the recent England sides at tournament level."
(Reporting by Aditi Prakash in Bengaluru, editing by Nick Mulvenney)
