Harry Kane scored his second England hat-trick and also set up Raheem Sterling’s strike as Southgate’s side cemented their position on top of Group A.
With three successive victories and 14 goals to their credit, the 2018 World Cup semi-finalists already look odds-on to qualify for Euro 2020.
Their next qualifier is against second placed Kosovo, who beat the Czech Republic 2-1 earlier in the day, at Southampton on Tuesday and Southgate claims it will provide a tougher examination than lacklustre Bulgaria could manage.
But it is next year’s tournament, which features several games in England, that Southgate was looking ahead to when he conceded he learns more from training sessions than he does these routine group matches.
“We have not had the tight, tense matches that the Nations League provided as of yet, that really we learnt so much more from,” Southgate said.
“So, therefore, we’ve got to do that in training and the challenge of training has got to be so high that we learn from those moments and we can see what the players are capable of.
“We have genuine competition for places, there are five or six guys you would expect to see on the team-sheet but outside of that it’s very difficult to call.”
Southgate knows if even Bulgaria can open up the England defence — as they did twice in the first half before squandering chances — then there is plenty for his players to work on before they can dream about winning the title.
“Have we progressed? Well, I think we have. We didn’t sit back after the World Cup,” he said.
“I know that you said that the Nations League was a disappointment. Once you are in the semi-final, you want to go on and win the thing. But also with unique circumstances, in that seven players arrived 48 hours before the game.
“I think we’re competitive with probably eight teams. I think that on our day, we can beat those teams, but equally the Dutch showed (in the Nations League) that they’re capable of beating us on their day and I think it really is a tight grouping of probably eight teams.”
While Southgate keeps his players on their toes, he knows he is blessed to be able to rely on the quality provided by Tottenham striker Kane and Manchester City winger Sterling.
Kane is the first player to score 25 or more goals in his first 40 appearances for England since Gary Lineker.
The England captain opened the scoring with a simple finish from Sterling’s pass and netted two penalties either side of Sterling’s strike from Kane’s cross.
“To be able to study him and the way he works at his game, for the youngsters he’s an incredible example. In those moments he has supreme temperament and technique,” Southgate said of Kane.
Sterling was by far England’s most creative force and Southgate was quick to praise his contribution.
“I thought he was outstanding. In the first half in particular when it was hard to find space,” he said.
“He will probably have the hump he’s only got one goal today because his mindset has shifted over the last two years.”
Kane has passed Geoff Hurst and Stan Mortensen on the list of England’s all-time goal-scorers.
While that was a “proud moment”, Kane admitted emulating 1966 World Cup winner Hurst by getting his hands on silverware is his real goal.
“That’s the aim. That is what you will be judged on at the end of your career,” he said.
“It’s great to get goals but England haven’t won a trophy for a long time. That is my goal as captain.
“We had a little taste of success at the World Cup. Obviously we didn’t go all the way but we have to use that as motivation at the Euros.”