The Three Lions defied low expectations to reach the final four of the tournament but, despite leading against the Vatreni in Moscow, were pegged back and eventually lost 2-1 in extra time.
Despite his desire to begin work on England's path to Euro 2020, Southgate concedes that he may never recover from the nature of his team's exit from the World Cup.
"We were 20 minutes from a World Cup final - that is going to live with me forever, there is no doubt about that," the former Middlesbrough boss told Sky Sports News.
"I'm conscious I've got to raise everybody but I'm up watching the game at four o'clock on Friday morning.
"I'm old enough now that I don't have to beat myself up unnecessarily. I think when I was a player I had a very simplistic mindset. I'm a lot more rational now. I can see what we have achieved.
"Your responsibilities lay elsewhere as a manager. It's different [from being a player] but no less painful, for sure. I've also got to get everyone else through the next few days."
England could still record their best World Cup finish since the triumph of 1966 if they beat Belgium in Saturday's third-place playoff.