England beat Tunisia 2-1 thanks to a stoppage-time winner from Harry Kane, whereas some of the teams tipped to win the tournament have struggled.
Argentina face elimination after winning just one point from their two matches and Germany lost their opening game.
But despite England’s narrow margin of victory over Tunisia, the manager was delighted with what he saw from his side.
“I think every team will want to improve but we hit a level that is comparable to anything that I’ve seen”, said Southgate.
“I’m very pleased with so much of what we’ve done, pleased with the mentality of the players and for keeping their patience.
“To win the game in the manner we did in the end was pleasing. It is important for them that they got a game under their belt, that they played well, that they experienced what it feels like to win with England in a big tournament.
“It’s a memory that will stay with everybody. Now we have to build on that.”
England’s next game is against Panama in Nizhny Novgorod on Sunday, where a win will all but seal a place in the last 16.