The Three Lions boss named his 26-man squad for the finals on Tuesday afternoon as preparations continue to ramp up.
With a mixture of fitness concerns and club commitments, Southgate is unlikely to have his full squad together until Friday at the earliest.
Preparations have certainly been trickier than they were for the 2018 World Cup, where Southgate guided an unfancied England into the semi-finals.
Now the 50-year-old knows more will be expected of him and his players, especially as a run to the final would see England play all-but one game at Wembley.
Asked if anything less than reaching the semi-finals would be deemed a failure, Southgate replied: “Yeah, it probably will.
“I think we’re realistic about that, we have to live with that expectation. We know the excitement around the team and it’s great, we’re now relevant.
“Expectations were lower (in Russia). We’ve got some exciting players and I don’t think these players are at their peak by any means. I think when I look at some of the players working with us it’s so exciting for England in the future.
“I’ve got to try to manage the expectations for the players. I accept the situation as a manager, there’s expectation, I have to deliver.
“We have to deliver as a group of staff, it’s not about me in terms of if we can be successful. But, of course, it’s about me if we fail. No problem, that’s the gig.
“But for the players, I’ve still got to bear in mind they are a young group, they have still got a lot of progression to make, some are now learning how to win things, being involved in big matches. It’s brilliant for their progress and opportunities for England, that’s what we want.
“Are we ready to win? Well, we’ve been to two semi-finals so the next step is to try to go further.”
Southgate insists he is continuing to improve as a coach as he heads back to Middlesbrough where he ended his playing career before taking his first steps as a manager in 2006.
“Then I was a 17-year-old apprentice like I was at Crystal Palace and now I’m probably a 23-year-old player,” he said when comparing his development in the dugout to his time as a fledgling footballer.
“I’ve only managed 200 games so in terms of experience, I’ve got a lot of experience now of as higher-pressured job as you can have experience of big matches with the national team.
“I still know that I’ll be better again in two years’ time and I’ll be better again in four years’ time because I’ve got the desire to improve, learn, reflect, get better and I want to be the best possible coach and manager that I can be.”