The Three Lions booked their ticket to next summer’s showpiece with an uninspiring 1-0 victory over Slovenia.
Southgate’s side are now guaranteed to top their group, while stretching an unbeaten run in qualification contests which dates back to 2009 to 38 games.
Expectation is always high around the England camp once they arrive at major tournaments, but there has been criticism of the current squad on the back of a forgettable showing at Euro 2016.
Southgate is hoping to have them better prepared for the next challenge, but has conceded that they are not yet at the same level as the very best in the world.
He told reporters after seeing Harry Kane snatch a dramatic winner against Slovenia: “It depends on where you would like to be and what is realistic about how quickly you can improve.
“What we want to do is maximise the abilities that we have and the capabilities that we have.
“Are we going to become Spain in the next eight months? No we’re not, but respectfully they have got a squad full of players that have won league titles and won Champions Leagues.
“We keep talking about world class players and until you are able to really perform and prove yourself on that stage then you can’t consider yourself in that company, but, our lads now have the chance to play on that stage again.”
England will wrap up their qualification campaign with a trip to Lithuania on Sunday.
They will then return to international action in November, with the next round of fixtures set to offer a greater examination of their credentials and offer an indicator as to any progress being made.