Southgate's side finished top of Group C despite a third successive underwhelming performance that was greeted with disdain by their fans in Cologne.
While Slovenia's players and fans celebrated wildly at the other end of the stadium after reaching the knockout stage, Southgate and his players were greeted with jeers when they trudged towards the England supporters.
Southgate was targeted by beer cups that missed the Three Lions boss but clearly left an impression on his psyche.
Coming after several days of criticism from former England players following a drab 1-1 draw with Denmark, the latest flop by Southgate's team threatens to create an even more toxic atmosphere as they head into the last 16.
Pleading with England's fans to create a positive vibe around the team, Southgate said: "I've not seen any other team qualify and receive a similar reaction. I'm very proud of the players for the way they handle it.
"The players kept composure in a game when they have come into it with a really challenging environment. It's taken me back to days when I was playing for England.
"I'm not going to back away from it. I understand the narrative towards me, better for me than it being towards them. It's creating an unusual atmosphere to operate in."
Southgate claimed England's relative success in his eight-year reign, which includes a runners-up finish at Euro 2020 and a World Cup semi-final appearance in 2018, had created expectations that his team are currently failing to match.
'I'm not going to back down'
"I think probably expectation," he said when quizzed about why the mood in the stands had changed.
"We have made England fun again over the last six years. It's been enjoyable for the players and we have to be very careful that it stays that way."
Southgate, whose contract expires at the end of this year, has hinted he will leave the England job if they don't win the Euros.
But he was adamant he remains in a positive mind-frame despite the barrage of negativity surrounding England's spluttering campaign.
"I'm in a really good place. I'm asking the players to be fearless and I'm not going to back down from thanking the fans," he said.
"The fans were exceptional with the team in the second half, that makes such a difference.
"It's so important they stay with the team no matter how they feel about me. I've been around England for 20 years. I've seen it. I get it."
The toothless Three Lions have won just two of their last eight games and have netted only twice in their three matches at the Euros.
But Southgate was grasping for signs of improvement in the Slovenia game.
"After what happened after the last game (against Denmark), I didn't think we would be free and liberated and score six goals," he said.
"But we have shown some encouraging signs. We pinned them back and had wave after wave of attack.
"Of course we would have loved a couple of goals. It's definitely an improvement on the last game. We have to build from here."
Having won the group, England could have a significantly easier path to the final than several of their title rivals.
But, understandably, Southgate was in no mood to look ahead.
"It's important to win the group because you control your own destiny," he said.
"It doesn't mean you get an easier tie but people can't accuse us of ending up with a tougher draw when we didn't win the group."
