England was fortunate to land on the weaker side of the draw allowing them to plot a route to the final, but Southgate's men are in danger of blowing a dream opportunity if they cannot find a way to get the richly talented team to start performing.
Sunday is a chance to hit the refresh button.
"That is the reality. And of course we have to deliver it," Southgate told reporters on Saturday. "So the fact is you go into a different mental state, everybody knows that knockout football is jeopardy.
"Everybody knows that on a given day, an opponent can make it really tough for you. You know that the quality of the opposition left is high, and so it changes the mindset. It's about how far can we go? We're trying to achieve something exceptional."
England were not the only top team that struggled in the first round, with Belgium, France and the Netherlands also failing to impress.
England captain Harry Kane, who has scored six goals in his last six knockout games, was asked if there is a palpable internal shift once elimination threatens.
"Naturally, you get physically stronger and you get sharper as you play more games," said Kane, who scored in the team's 1-1 draw with Denmark. "Not just for me, but a lot of the players come into their peak sharpness at the knockout stage.
"This is knockout football now. These tournaments come round quickly and they go quickly. We are going to need a big performance. Less talking now, it's time to show what we can do."
Southgate has a squad in full health apart from Luke Shaw, who is not ready to start but might be able to come off the bench in what would be his first game since February.
The team enjoyed a break after their 0-0 draw with Slovenia on Tuesday that capped the group stage.
"They had a day off their feet and not think about football which is important in a tournament," Southgate said. "They have played golf, whatever they wanted to do. There's no science about that but you have to remind yourself it's about enjoyment."
There have been a few big events within the squad too, he added, as Phil Foden's partner gave birth to their third child while Jude Bellingham (21) and Eberechi Eze (26) both celebrated birthdays on Saturday.
Bellingham has shouldered weighty expectations after his remarkable debut season at Real Madrid, but drifted out of the Denmark and Slovenia games after a strong first half in their opener against Serbia.
"(His birthday) is a reminder of his age and how well he deals with all the expectation around him at a remarkably young age," Southgate said.
"I can think of few players who've had to live in that world and I can understand that his world is different to most of the 21-year-olds that I know. So he's dealing with that exceptionally well."
England, who finished top of their group, are expecting a tough challenge from Slovakia, who advanced as one of the best third-placed teams.
"They have some great players," said Kane. "They like to press high and make it difficult for the opponent. It's going to be a tough game. We are expecting a physical team with a lot of quality."
