The Three Lions squandered a second-half lead given to them by a Harry Kane penalty with just seconds of normal time remaining at the Spartak Stadium.
Southgate insists that he never lost faith in his players, who has has praised for remaining in control of the match in the opening 90 minutes.
"It was a night where I knew we'd get over the line. We had the resilience and the belief to get over the line, whatever it takes," he told reporters at his post-match press conference.
"We had total belief in what we were doing, right through to the end. Even when our first penalty was saved, I've seen enough shootouts where the first penalty missed isn't the key one.
"I'm proud of the way my team played. I thought we controlled the game in the 90 minutes, played with great discipline, we were very composed with the ball and in a big game that was impressive from a young group of players. It's a special night for everybody involved."
England will now face Sweden in the quarter-finals, while one of Russia and Croatia await in the final four if they progress through.