The Three Lions are at St. George’s Park preparing for their trip to Lithuania on Friday and the subsequent journey to Moldova next Tuesday.
And despite having already secured top spot in their group and a place in the draw for the play-offs, Southgate believes that his squad have the right mentality with which to approach their final matches.
He said: "We're talking a lot this week about maintaining our standards and what's needed for an elite team.
"That's the culture we're trying to create because of the standards that these boys have got every day really.
"They're starting to recognise what's needed to be a top player so when you transfer your work on the training ground onto the match pitch, if they do that, then they'll be fine."
England will be one of 14 teams in the draw for the play-offs on Friday 12 September, which consists of the ten group winners and the four best second-placed nations.
The seven play-off winners will then join host nation Czech Republic in the eight team line-up for the European Championship Finals next summer.
And with England expecting a tough two-legged encounter with whoever they’re drawn against, Southgate believes his squad’s trip to the Toulon Tournament earlier this year will have helped them to prepare, facing opposition from the likes of Brazil, Portugal and Colombia.
"That's why we did what we did in the summer, so the players could recognise the level that was needed," he explained.
"Those are the experiences that we're going to face. I think there's only Portugal and ourselves who are confirmed as qualified at the moment and the others are all there or thereabouts.
"So we know we're going to face a really top side next month and we need to prepare them for that."
As things stand, Denmark, Netherlands, Spain, Croatia, Germany, Poland, Serbia and France are the others teams topping their groups with the likes of Russia, Ukraine and Belgium also challenging.
Southgate added: "There's going to be seven or eight top teams in the draw, without a shadow of a doubt, but there will be a few unknowns as well.
"Poland are doing well, and for all we know, Poland's group this year could be stronger than Spain's.
"Some nations just have a strong year group of players which sometimes throws up surprises if they have a good group of players."
The England squad are training at St. George’s Park until Thursday, when they fly out to Kaunas for Friday’s first game with Lithuania.
After that, they remain in Kaunas until Monday when they move on to Tiraspol for Tuesday’s group closer against the Moldovans.