Danger lurked throughout the 32-team draw for the World Cup but England avoided the toughest opposition as they were drawn, by Diego Maradona, in Group G alongside Belgium, Tunisia and the World Cup debutants Panama.
Southgate pointed to England's premature exits from the last World Cup and Euro 2016 as reasons for limiting expectations.
"We don't really know how far this team can go because it's a team that a lot of its best years might be ahead of it, but it's a team that is hungry wants to do well and has energy, and we may surprise a few people".
"We've got six days of rest after our first game, which if they are anxious about travel, that shouldn't be an issue".
We're all together in the games room, playing pool, having a laugh and I think it is really bringing the squad together nicely.
With Belgium able to call upon Premier League stars such as Chelsea's Eden Hazard, Manchester City's Kevin de Bruyne and Romelu Lukaku at Manchester United, they are now ranked fifth in the world, 10 places higher than England.
Walker said: "It feels like club football now".
Belgium head coach Roberto Martinez says he is excited about facing England at the 2018 World Cup.
I spent 21 years in the British game. They will then travel to Novgorod to face Panama on 24 June before the final group match against the top seeds Belgium in Kaliningrad on 28 June.
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".
He said: "They are always a contender to do well at tournaments, but they do seem to lack something when it comes to the latter stages".
France, Australia, Peru and Denmark make up Group C, with Group D perhaps the closest to a so-called "Group of Death" as it contains Argentina, Iceland, Croatia and Nigeria.
"Being involved in that game - the colour and the atmosphere around it - was one of the best days of my life", he said.
Maaloul, appointed in April for his second spell in charge, played 74 times for his nation but never made it to a World Cup.