England, which has reached one major semi-final and one final under Southgate, will open its campaign with a first-ever meeting against Iran on the tournament's opening day on November 21.
England will then face United States in a repeat of its opening game at the 2010 World Cup, while its final group match could see it face a home nations rival in Wales or Scotland, who will compete with Ukraine for Europe's final qualification place in a play-off that has been delayed due to Ukraine's ongoing conflict with Russia.
On paper, Group B looks set to present a smooth passage to the knockout stages for England but Southgate, who led the Three Lions to a first World Cup semi-final since 1990 four years ago, is not looking any further ahead than the group stages.
"The first two teams we've not played for quite a while," Southgate told BBC Sport. "The third is a total unknown but throws up a possible British derby. We know what they're all about, we've had plenty of them!
"For us, we're in on day one so it's quite clear now what our program looks like, with the end of the Premier League season and getting out here as quickly as possible."
Asked if that knowledge gave England more time to prepare for possible knockout games, Southgate responded: "It does, but we've got to get out of the group.
"What we've done well is approach these tournaments by looking at the group.
"The first objective is to get out of the group, regardless of the opposition, and then you build from there.
"When you're seeded, you get the advantage of missing out on those big six or seven teams. For most of the first seeds, they'll be pleased with the group they get.
"There's obviously some really high ranked teams in Pot Two, and the US in particular, I know Gregg Berhalter quite well, we've met a couple of times and had long chats about things.
"They've got some very good players and we know what they could be capable of as a nation. That one, in particular, is an intriguing one."
Furthermore, being drawn into a World Cup group with United States for a third occasion represents the first time that England has been in the same group as one particular nation at three separate editions of the tournament.
England captain Harry Kane, meanwhile, was glad to see that the Three Lions will open their campaign on the first day of the tournament.
The decision to host the World Cup in Qatar has faced strong opposition from many quarters.
Southgate, who made his opposition to any boycott of the tournament clear during the recent international break, expressed his desire for the World Cup to drive substantive change in the Gulf state.
"We'll continue to speak to people here," he added. "We've got to build relationships here to be able to highlight any change that we'd like to make.
"It's important to do that in the right way. Today my focus is just on the draw and working out what that all means really."