England won their first World Cup penalty shootout in Moscow on Tuesday , Eric Dier slotting home after Jordan Pickford had made an exceptional save to deny Carlos Bacca.
It came at the culmination of a frantic, hard-fought encounter - Harry Kane's 57th-minute penalty putting England ahead before Yerry Mina restored parity in stoppage time.
And Southgate, who says he is still haunted by his penalty shootout miss against Germany at Euro 1996, believes his young England side have now reached a watershed moment.
"That will never be off my back. It is a moment that will live with me forever, sadly," Southgate said of his miss 22 years ago.
"But today is a special moment for this team, and that hopefully will give belief to the generations of players that follow, because they can see what is possible.
"In life you can't be hindered by history or expectations. The young players are showing that, enjoying the tournament, and we are looking forward to preparing for the quarter-final.
"We've talked about the team making their own history and I think they've bought into everything we've tried to do with them.
"We've got to capitalise on that now. I'm already thinking about the next game, we'd have liked a week to enjoy it but we haven't got that, because Sweden are a team I respect hugely.
"That's a hugely difficult game for us. At the moment we're as high as a kite, having to recover."
Pickford will likely go down as the hero for England, although the Everton man had come under fire in the build-up to the game following his failure to keep out Adnan Januzaj's winning goal for Belgium in the Three Lions' final Group G fixture.
Belgium goalkeeper Thibaut Courtois went as far as to say Pickford was too small, but Southgate was full of plaudits for the 24-year-old, who had made a fantastic save to keep out Mateus Uribe's strike prior to Mina's equaliser.
"Yes, the save [from Uribe] was a top-class save. I'm surprised he could reach it, given his height," Southgate quipped.
"His athleticism around the goal is excellent. Again, he executed the plan in the shootout.
"We studied all of their penalty takers and great credit to their collective of staff and to him for taking on board that information and preparing in the right way. You don't always get what you deserve in life, but tonight we did."