England lost 3-1 to Netherlands in Guimaraes on Thursday – Southgate's men missing out on a spot in the inaugural Nations League final.
Marcus Rashford had given England the lead via the penalty spot in the first half, however, Matthijs de Ligt equalised before defensive errors gifted Netherlands two goals in extra time.
It was an all too familiar feeling for England, who lost in the semi-finals of the 2018 World Cup, but manager Southgate was upbeat post-match.
"We were talking before the game as a group of staff about the incredible games England played in tournaments, the twists and turns, it's hard to take it all in," Southgate said.
"I thought it was a really high level of opponent, they posed us problems in the first half without creating clear chances. We solved those problems but throughout the game we made too many mistakes in our third, partly due to their pressure but partly just errors. We got into the lead and a poor goal from a set play, then we responded with our best spell, we changed the shape and got Raheem into the pocket as a 10 and we started to control the game.
"We scored, thought we'd scored, it was really fine margins, but we still controlled the game until the second goal. Last two goals are very difficult errors to account for.
"Incredibly proud, they gave absolutely everything, it's painful for them and everybody but a night where we learned so much.
"Some individuals really stood out, Declan Rice playing in that environment, Ross Barkley was outstanding, Raheem. So, tough to take in the end as you get to another semi-final it should be a positive but everyone leaves deflated.
"I have to look at the bigger picture of what the players have given."
After a hard-fought 90 minutes, it all went downhill for England in extra time as mistakes proved costly in defence.
John Stones' error led to a Quincy Promes shot deflecting in off Kyle Walker, then Ross Barkley's mistake allowed the Netherlands substitute to secure a final berth against Portugal.
"I think we've had some players at the end of the season with difficult amount of minutes, others have had the opposite," added Southgate after being asked about Stones. "I think fatigue has played a part, a lack of sharpness, but I'm asking them to play in a way that puts them under huge pressure at the back.
"We wouldn't have reached the semi-finals without playing that way, to become a top team, Holland play like that too and made a poor error. I have to be there to support John, he'll get criticism, but the way we ask them to play they take huge strain on their shoulders and they are courageous to do that.
"It's the way we can and should play. That's not why we lose, they were uncharacteristic and not errors we would make, it wasn't risk it was poor execution and the last one was just fatigue. I have to not over-react and need to be there to support them in a difficult moment for everyone."