The Three Lions head coach said after the game that he is now thinking about the clash with Sweden in the next round, and is not ready to go home just yet.
"We played so well in the 90 minutes, We showed resilience to come back from huge disappointment and kept calm. It's huge credit to all our players and staff," Southgate told ITV Sport.
"Shootouts are tough. We had talked long and hard about owning the process of a shootout. They kept calm. The players have taken it all on board, it's a special moment for us.
"We looked at technique, how we needed to be as a team, the goalkeeper's role. A special moment but now I'm thinking about Sweden.
"They have created their own story and made history. I don't want to go home yet."