The Three Lions are bidding to reach a first major tournament final since 1966, having fallen just short at the 2018 World Cup in Russia, where they lost in the semis.
England then suffered more semi-final disappointment in 2019 as they were beaten by Holland in the Nations League.
But Southgate insists the experience gained on those two occasions will help England as they prepare for their Wembley showdown with the Danes
He told BBC Sport: "We are better prepared for this semi-final in that we've lived it before. We've had another two semi-finals prior to this one.
"And although that doesn't determine winning or losing a game of football, there are a lot of factors that we are aware of and we have dealt with before that help you to prepare in a better way.
"In Rome, it was important to go and thank the fans who turned up in such numbers, but everybody was quite calm about what was going on and we knew we hadn't achieved what we want to achieve yet."
England's full squad of 26 trained at St George's Park on Tuesday morning before heading south in the afternoon.
Bukayo Saka was again with the group, having recovered from the knock that saw him omitted from the squad against Ukraine on Saturday as a precaution.
Southgate also highlighted the "very special" chance his side have to bring happiness to the country.
He added: "The opportunity to bring happiness and create brilliant nights for our fans, our nation, is a very special one that you have when you play with England.
"England matches are events that bring families together, that bring communities together, and they are matches that you remember where you were.
"Some of the nicest messages you get are that people appreciate how the players have been, that they feel they can connect with them. They should be very proud of that."