Southgate's men were pitted against Tunisia - a team they beat at the same stage at the 1998 World Cup - and tournament debutants Panama in Friday's draw at the Kremlin in Moscow.
The Three Lions were also handed the tricky proposition of a game with Belgium, who boast what is seen as a golden generation featuring the likes of Romelu Lukaku and Eden Hazard, in Kaliningrad in their final Group G game.
That could be seen as a match to decide the winner of the group, but, with England having finished second in a group containing United States, Slovenia and Algeria in 2010, before failing to get out of a group also boasting Italy, Uruguay and Costa Rica in 2014, Southgate feels a team that lost to Iceland in the last 16 of the European Championship last year can ill-afford to look beyond any opponent.
Speaking to BBC Sport, Southgate said: "We've been good at writing teams off and then getting beaten by them haven't we? We've got to be prepared for every game."
Southgate was part of the England team that defeated Tunisia 2-0 in the opening game of the 1998 tournament and added: "Remembering the Tunisia game in 1998, it was the first thing that went through my mind. It was a fantastic day and it's nice to be able to relive that.
"We haven't done as much preparing on the African teams yet so now that's what we can focus in on."
Belgium are 10 places ahead of England in the world rankings, but both teams went unbeaten through qualifying and their encounter on paper is one of the ties of the group stage.
"They're an outstanding team," Southgate said of Roberto Martinez's side.
"They're ranked where they are in the world because of the quality they've got. They're top, top quality opposition.
"Through the qualifying campaign you don't think about days like today where everything hits home, but that's the beauty of the World Cup.
"When you look at old videos and goals it takes you back to the pureness of football. Now, the country knows what's coming and they can get excited.
"That's why it's so fantastic to be involved again. For me personally it's been an incredible journey. To play for my country in a World Cup is an incredible honour, to lead my country there as a manager is beyond that."