The highs of an opening 6-2 thrashing of Iran were quickly forgotten as Southgate's side laboured to a performance labelled "terrible" by former Manchester United midfielder Roy Keane.
"I knew it would be difficult for us after such a high (against Iran) to replicate that type of performance, so I'm really pleased with how the players have applied themselves," Southgate told ITV.
"Some of our quality in the final third could have been a little bit better, but we've shown great resilience to defend against an opponent that kept asking questions and we've just not been able to open them up with that really clear-cut chance.
"We didn't quite have that same zip but this is going to happen with tournament football. We're not going to roll through a tournament and sweep through everybody without having nights like that where you've got to show different qualities to get the result.
"Silver medal today was a point because it puts us in a really strong position in terms of qualification. If we can win our last game (against Wales on Tuesday) we win the group.
"The objective is to get out of the group, you get three games to do it. We've done it in two games the last two tournaments, but it's very unrealistic to expect that every time."
Captain Harry Kane admitted England were far from their best but told ITV: "We had some good spells with the ball, created some good positions, just didn't quite have the final product today, but a clean sheet puts us in a great position in the group.
"(It was) the complete contrast to the game against Iran when we took our chances really well. Today we had two or three opportunities and didn't quite put it away. We played a tough team and we move on.
"We know we can play better than that for sure. No game is easy in a World Cup. After our first performance people thought we were going to landslide every team we play, but it's not the case."
Former Manchester United and England defender Gary Neville was surprised not to see Phil Foden in action.
"Tournaments are very rarely a bed of roses all the way through but it was poor. We wanted a lot more from England," the pundit told ITV.
"Our midfield didn't click tonight, I thought we looked tired. I was disappointed not to see Foden - for me that talent is huge. For him not to be in a starting XI and not come off the bench was interesting."
Neville's former team-mate Keane also wanted to see Foden brought on, adding: "The subs that did come on didn't really have an impact.
"England looked leggy, one-paced, short of ideas, even set-pieces you never felt they had a goal in their locker from that - actually a terrible performance."