Southgate’s side will discover who will join them in Group D when the draw is made in Bucharest on Saturday.
England could end up facing both holders Portugal and world champions France but will have home advantage, with all three of their group games taking place at Wembley.
And Southgate feels their run to the World Cup semi-finals in 2018, and to last summer’s Nations League finals, means other teams should be worried about facing England.
“I think we’ve gained some respect and I think people would view us as a threat, which certainly wasn’t the case ahead of Russia,” he told BBC Sport.
“We also know we have got to improve to another level. It’s hard to assess exactly where we are after this qualifying campaign, but if we looked at the World Cup semi and the Nations League semi, we’ve done all we could in terms of qualifying with the most goals in Europe, so we are on a good track.
“The difference on one day between any of the top 10 teams is so marginal in football.
“It’s different in rugby where only four or five are contenders, with us in the Euros it’s always been more random than a World Cup – you could look at any one of 10 teams and think they could win it.”
England would face Scotland at Wembley should Steve Clarke’s side come through their play-off semi and final in March next year.
The Scots face Israel at Hampden Park and would then travel to Norway or Serbia for a one-off match to secure their place. They would play their other two Group D matches in Glasgow.
Wales, who booked their place in the finals with victory over Hungary earlier this month, know they will go into Group A or B.
Group A features Italy, who will play all three of their group matches in Rome. Wales are in pot four, so could also be joined by France and Portugal in that group.
Group B only has one slot left to fill, with Belgium, Russia and Denmark already in it. Wales would play one match in Copenhagen and two in St Petersburg in that eventuality.
Northern Ireland and the Republic of Ireland are fighting for one place in the finals when play-off path B takes place in March.
If either emerge victorious in that four-team mini-tournament, they will head into Group E alongside Spain, with matches in this pool to be hosted in Bilbao and Dublin.