Hodgson began his managerial career with Swedish team Halmstad in 1976 and has held roles with Switzerland, Inter Milan and Liverpool among others over the past 50 years.
His time with England ended in 2016 after a disappointing exit from the European Championship, losing to Iceland in the last 16.
“It was a really bad moment,” Hodgson said.
“It’s extremely difficult because I had a quite strong belief that we would do well and I thought we would beat Iceland.
“I think the team in 2016 had the potential to do what the England team is doing now because there was a lot of young players coming through and you could see the potential of the young players.”
Hodgson told the media that he was resigning in the post-match news conference.
“I remember seeing the disappointment in Roy and I think we knew then that that was going to be the end of him,” Rooney said.
“I was also starting to think potentially this is the end of my own career as well.
“I think that moment in that dressing room after the game was the worst I’ve ever felt.”