Jones was sacked by the Rugby Football Union earlier this month following a year in which England won only five of their 12 tests. He was replaced by former captain Steve Borthwick.
Jones, who helped England win three Six Nations titles and led them to the 2019 World Cup final during his seven years at the helm, said he could "feel the change in the wind".
"When you have been coaching for a while you feel when your support is starting to wane and I knew we had to have good results in the autumn," the 62-year-old told the BBC.
"I continued on coaching as well as I could and we had a plan to peak at the 2023 World Cup, but unfortunately we didn't get the opportunity to finish that.
"I thought it was coming. There was a discussion but when boards make that decision, they already have it firmly in their mind.... I didn't think I was coaching poorly and that is all I could control."
Jones was tight-lipped when asked if he had spoken to Rugby Australia about taking over from Wallabies boss Dave Rennie but he said he still had much to offer the game.
"It's not about coaching England's rivals, it's about adding to the game. I love the game and I love coaching," he said.
"As you get a bit older, as I am, you just want to leave things in a better place. I just want to share the great experience I have had, particularly with coaching players and teams."