England are the only European team to have reached the semi-finals in each of the last two major tournaments - the 2018 World Cup and Euro 2020
The Three Lions begin their World Cup campaign against Iran on Monday.
"Our challenge is to give our supporters a tournament that is memorable," said boss Southgate.
"Our country is going through a difficult spell, in the middle of an economic recession and life has been difficult for a lot of people."
Southgate added: "We want them to have a journey with the team that brings real happiness."
England go into the game as favourites but their boss says his players need to be patient if they do not score early on.
"Our team have been pretty creative and successful in breaking those sorts of challenges," said Southgate. "We know we mustn't be frustrated if it takes us time to score, confident with teams playing against Iran, difficult to score goals.
"This team has been through lots of difficult challenges. You need to respond in the right way and that's what we'll aim to do this tournament too."
Iran coach Carlos Queiroz, who had two spells as Manchester United assistant boss, says England are among the contenders to win the tournament.
"What can I say about England? One of the top national teams in the world," he said. "They are serious candidates to be in the final position, why not a contender to be the world champion?
"They reached a wonderful position in the last World Cup and Euros. They have a storm of talent.
"I worked with the generation of Rio Ferdinand, Paul Scholes and David Beckham but this national team is really different because they have a realistic approach to any single game which makes them very, very dangerous."
James Maddison was recalled to the England squad for the World Cup after a three-year absence
England will be without midfielder James Maddison and defender Kyle Walker for Monday's game.
Maddison has yet to train in Qatar as he nurses a knee problem picked up playing for Leicester last weekend, while Walker is still working his way back to fitness after groin surgery.
Iran are hopeful Sardar Azmoun will be fit for their tournament opener. The Bayer Leverkusen forward has not played since suffering a calf injury at the start of October.
-- Courtesy of BBC Sport