Displaying impressive character at the end of a game that had started with no little skill, captain Harry Kane headed home his second goal to secure the Three Lions a deserved 2-1 win in Monday’s Group G opener.
It was England’s first winning start to a major tournament since 2006 and puts them in a strong position to reach the last-16 heading into Sunday’s match against minnows Panama in Nizhny Novgorod.
There appears little chance of complacency seeping in, though, given Southgate’s focus and the players’ hunger to improve.
“There are always things (to improve),” said the England boss. “We are a team that are improving and developing, and therefore there will always be things that we can get better at.
“We’re a long way from perfection. What pleased me is that there has been a long period of work gone into (Monday’s) result from all the players and all of the support team.
“If you don’t get the win, even though you’ve done so many things right, that can breed a little bit of doubt.
“Of course there would be a different feel externally, so the next four, five days would be a little less comfortable for people.
“What we’ve got to make sure is we enjoy it, but we don’t have comfort for the next four or five days. We have got a job to do.
“We have to prepare as perfectly for Panama to make sure we get the result in that game we need.
“I think the players know it’s hard to win a match in the World Cup against any opposition and Tunisia were opposition we respected.
“But Panama for 45 minutes were obdurate opponents against Belgium and we’ll have to prepare 100 per cent right to win it.”
It took until the second half for Belgium to break down Panama’s resolve, going on to run out 3-0 victors and sit atop Group G on goal difference.
Patience was key for Roberto Martinez’s men in that match, just as it was for England when grabbing three points against Tunisia.
Perhaps it was inevitable that England would taper off given the lack of experience within the group, but the players’ composure and focus should not be underestimated.
Former Sheffield United and Hull City centre-back Harry Maguire ended particularly strongly given his nervy start, earning high praise from former England defender Southgate.
“I think his potential is huge,” he said of the Leicester centre-back, who provided the assist for Kane’s late winner.
“He’s probably the one player – him and (Jordan) Pickford – who haven’t played in cup finals or on big-stage Champions League games in the past.
“Maybe it was a voyage of discovery for him (more) than some of the others, but he has great composure, really good defensive qualities.
“Most things land on his bonce in both penalty areas and he’s got a really lovely, calm temperament.
“For me, he has outstanding potential and I hope (the game) has given him a lot of belief.”
Maguire was among nine World Cup debutants in the starting line-up against Tunisia.
It was the same opposition that Southgate made his bow against on the world stage 20 years ago, when Glenn Hoddle’s men opened with a 2-0 win.