Southgate hails 'incredible job' as England reach Euro 2020 final
England came from a goal down before Harry Kane converted the rebound from his missed penalty in extra time to send his team through to a showdown with Italy.
"I'm so proud of the players," Southgate told ITV.
"It's an incredible occasion to be a part of -- we knew it wouldn't be straightforward, we said to the players we'll have to show our resilience and come back from some setbacks, and we've done that tonight."
England conceded their first goal of the tournament when Mikkel Damsgaard drilled a free-kick past Jordan Pickford, but the hosts soon equalised as Simon Kjaer turned into his own net.
"I felt we would get there -- I knew we would have different sorts of battles because Denmark are so underrated as a team," said Southgate.
"They did cause us a lot of problems, when you've waited as long as we have to get through a semi-final, the players, considering the limited international experience some of them have had, they've done an incredible job."
Southgate credited Kane for keeping his nerve after having his penalty saved initially by Kasper Schmeichel.
"There's nobody you've rather have on it, but you're up against a great goalkeeper who he's obviously faced a lot of times -- but thankfully that's now immaterial."
After falling to Croatia in extra time in the 2018 World Cup semi-finals, England made sure there was no repeat slip-up in front of almost 65,000 fans at Wembley.
"The most pleasing thing is that we've given our fans and our nation a fantastic night, and the journey continues on for another four days," said Southgate.
"To come through that sort of a night -- we suffered in Moscow (in the World Cup semi-final) and on a night like this we've managed to put things right."
But he was quick to shift his focus to Sunday's final against an Italy side on a national record run of 33 matches unbeaten.
"We're in the final and we've got to enjoy that fact, but there's one more massive hurdle to try and conquer."