Eventually England came through 2-1 winners in extra-time, but not before putting their fans through some anxious times as they dominated the second half against Denmark, but struggled to beat an inspired Kasper Schmeichel.
"I felt calm in the lead-up to the game because I felt the players with what they've been through over the years were ready," said Southgate, whose side were playing their third semi-final having reached the last four in the World Cup and Nations League. "You're never 100 per cent sure how they will react in the difficult moments but we responded well."
England went behind to the first goal they had conceded in the tournament, a Mikkel Damsgaard free-kick, but equalised through a Simon Kjaer own goal before Harry Kane had a penalty saved, then put in the rebound after 105 minutes.
"We were so smooth through the quarter-final and relatively unscathed throught the second round so we knew at some point they were going to concede," said Southgate.
"On the balance of play when you look at the number of saves we forced the goalkeeper to make and the long periods of the game where we were the biggest threat."
Of the atmosphere generated by a crowd of over 60,000, Southgate said: "I've not heard this new Wembley like that ever."
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