It was a tough game for England against their World Cup conquerors at Wembley, but they should admirable character to grab two late goals to book a semi-final spot in the inaugural competition next summer.
There were plenty of positives to take from the achievement, but Southgate was particularly pleased with his side's attitude and also the continued connection with the fans - highlighted by a rocking atmosphere at Wembley.
"We didn't discuss the relegation at all. We just saw this as an opportunity, it was effectively a quarter-final," Southgate told Sky Sports.
"None of us knew what this tournament would be like but the atmosphere in the stadium and the emphasis on the game because of what has happened in the last few months really rose as we went forward and that's great because we had to live with the pressure of playing at home.
"We have come out of an incredibly tough group, in terms of form and world ranking ours is the toughest.
"We haven't just sat back after the summer and preened ourselves, the players have progressed.
"I think people can see the style, people are starting to believe in what we are doing but the biggest thing for me is the connection with the fans - I've not seen new Wembley like that since I've been in charge."
England profit from long throw routine
Southgate allowed himself a wry smile at the way they got themselves back into the game having earned a reputation at the World Cup for the style of football they played.
"I thought we dictated a lot of the game and had some really good chances in the first half and should have been ahead and then we let quite a soft goal in," he added.
"That is a real test of resilience and patience. We rode our luck a little but with their counter-attacks and one cleared off the line and for all the good football we played, we scored from a long throw and a set-play.
"Maybe we're not a new England, maybe we're the England we've always been!"
Kane hoping to make fans proud
Man of the match Harry Kane was relieved to have ended his seven-match international goal drought as he sent his side to Portugal next summer.
"It felt good. It has been one of those spells for me personally, but that is what it is about. (We) stuck at it, stayed calm. We deserved to win," he said.
"We were disappointed we didn't take out chances but we were creating chances.
"We said after the World Cup we wanted to keep progressing and the only way to do that is win games against big opposition.
"We want to make everyone proud. We are going to enjoy it so I hope the fans do too."
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