The 69-year-old was in charge of the Three Lions for four years after replacing Fabio Capello in 2012, winning three of his 11 games in charge at major tournament finals.
He subsequently quit the role after England were knocked out of Euro 2016 by Iceland, who were among the lowest-ranked teams in France.
"I don't know whether you ever get over things that cause you pain," Hodgson told BBC Sport.
"You probably shouldn't relate it to death but where grieving is involved and things matter to you a lot, do you ever get over it?
"I suppose there's always going to be a scar but I don't intend to grieve any longer and I certainly don't intend to let it haunt me."
Gareth Southgate is currently in charge of England as the home nation bids to reach the 2018 World Cup in Russia.