Substitute Ollie Watkins scored in the 91st minute to send England through to their second successive European Championship final with a 2-1 win.
Their overall performance was an emphatic answer to the criticism heaped on his side for some earlier languid showings.
"We all want to be loved, right?" Southgate told a press conference. "When you are doing something for your country and you are a proud Englishman, when all you read is criticism it is hard. To be able to celebrate a second final is very, very special."
"We have given people some amazing nights, some of the best nights in 50 years."
Southgate, who took over in 2016, has now led them to at least the quarter-finals in the last four major tournaments, the only European side to achieve this feat.
They lost to Italy on penalties in the Euro 2020 final but now have the chance to go one better against Spain in Sunday's showcase in Berlin.
"It shows the more modern England way but also the resilience and character of the group. Ollie Watkins has trained like that every day. He has trained for his moment no matter how frustrated."
"They had each others' back, they bonded so well and tonight it was an example of that."
England needed penalties to overcome Switzerland in the last eight before the late winner on Wednesday, and Southgate said his team had learned from knockout matches since the 2018 World Cup in Russia where they lost in the semi-finals to Croatia.
"We are more calm going into the knockout games. In Russia we had not won a knockout game in 10 years," Southgate said.
"To be able to take the team to the first final overseas I am immensely proud of that," he said.
England won the 1966 World Cup on home soil while the Euro 2020 final was also held at Wembley.
They will now face the form team of the tournament Spain, who have all their matches in Germany.
"We will have to get the ball off them first," Southgate said of their next opponents.
"It is not as simple as us having the ball and making them run. We have to be exceptional with the ball and without it. They have been the best team."
"We are starting to show a better version of ourselves," he said, adding they had one less day than Spain, who beat France on Tuesday in their semi-final, to prepare.
"But we are in there with what we have shown to this point. We have as good a chance as they do. We have come here to win it. It is a huge task but we are still here and fighting."
