Tuesday’s victory has seen hope and expectation increase that this could finally be the year that England add to the World Cup triumph of 1966, when Sir Alf Ramsey’s side played all six of their games at the national stadium.
Southgate’s men would play all but one of their matches at Wembley if they reached the Euro 2020 final, with Saturday’s quarter-final against Ukraine at the Stadio Olimpico the only game they would play away from home.
Logistical headaches and hot weather replace home comforts and a partisan crowd, but the England boss believes that could provide the kind of shock they need after the Germany triumph.
“I think there was clearly a big emotional toll from the game and everybody enjoyed the day but, even in the dressing room afterwards, the players were already talking about the next game and the need to prepare well,” Southgate said.
“So we have shifted the mindset quickly onto that next challenge.
“We’ve achieved one challenge but that’s not the Everest we set ourselves, really. We want to push on from where we’ve got to now.
“I think the psychological freshness is key. We’ve obviously got a strong squad as well.
“It’s actually, for us, probably a good thing to be going away now. It would’ve been very hard, three days later, to replicate that experience at Wembley.
“So now we’ve got a different sort of test.
“We’ve got to go away from home, play a good team, without many English fans in the stadium, so it’s all about our group, it’s all about our team and what we do, and the energy and focus that we create.”
All 26 players trained at St George’s Park ahead of Friday afternoon’s flight to Italy, where they are overriding favourites with bookmakers to progress to the semi-finals.
Ukraine are 24th in the FIFA world rankings – 20 spots below England – and progressed to the last 16 as the luckiest third-placed side.
Andriy Shevchenko’s men beat 10-man Sweden 2-1 in extra-time on Tuesday and Southgate is ready for a tough evening.
“I think we know that Ukraine are a good side,” he told UEFA. “I’ve been really impressed with what Andriy’s done with them.
“They had a couple of sticky results through the autumn, through the Nations League but they’ve bounced back, and they got a very good result in France, in the World Cup qualifiers and, again, this week against Sweden.
“So if we give them space to play, they’ll play, and they’ve got some dangerous forwards.”