Harry Kane's goal in second-half stoppage time ensured England took all three points from their Group G opener and Southgate praised his substitutes for adding energy and threat late in the game.
After Kane opened the scoring in the 11th minute, England were guilty of wasting a number of first-half chances to extend their lead before Ferjani Sassi levelled from the penalty spot.
The introduction of Marcus Rashford and Ruben Loftus-Cheek revived Southgate's attack in the closing stages of the game and the England manager told The Guardian: "The guys who came on had a different threat.
"The freshness of Marcus and Ruben brought energy and a different threat to the one we'd posed.
"We talked about this with the players at St George's Park over the last few weeks before coming to Russia. The way we'll change the game is by bringing on a different profile of players, who carry a different sort of threat."
England's forthcoming opponents Panama were beaten 3-0 by Belgium in their opening game but Southgate warned his players not to underestimate Hernan Dario Gomez's team.
With five days to rest and train ahead of Sunday's game in Nizhny Novgorod, the England boss said: "We have to prepare as perfectly for Panama as we did here to get the result we need. It's hard to win a match in the World Cup against anyone.
"Panama were obdurate opponents against Belgium for 45 minutes, so we'll have to prepare 100 per cent for that game to get the right result."
England are unbeaten in competitive matches since their 2-1 defeat to Iceland at Euro 2016, but Southgate called for patience as his young side finds its feet in tournament football.
"We are a team who are improving and developing," he said. "There will always be things we can get better at.
"We're a long way from perfection."