Harry Maguire and Dele Alli scored in each half to see off stoic Sweden, with either hosts Russia or Croatia next for the Three Lions.
Southgate paid tribute to the way the squad responded after coming through the drama of a penalty shootout win over Colombia to reach the quarter-finals.
“We knew it was going to be such a different game from the other night, to come back having had extra-time and penalties, with the emotions of it to lift ourselves through a completely different test,” he said.
“It was always a scrappy game where we had to withstand a lot of physical pressure, but the resilience of the team and togetherness of the team was crucial.”
Southgate paid tribute to a collective effort, on and off the pitch. “I cant speak highly enough of the whole squad and whole group of staff because it is so united in there,” he said.
“The level of work has been great and their commitment to each other, you don’t get through with just 11 players. They are all top people and are the reason we are in the semi-final just as much as any other.”
Southgate admitted playing against Russia in Moscow would be “an incredible game” to be involved in, but will take things one step at a time. “We will enjoy tonight, I hope everybody at home enjoys tonight because as we know, it is not very often that it has happened,” he said.
“All I know is the managers who have got to semi-finals (with England) are ones I hugely respect and to be involved at this stage with England now is an incredible feeling.”
England’s tally of 11 goals equals that set at the 1966 World Cup, which they won as hosts.
Captain Harry Kane, who leads the race for the 2018 Golden Boot with six goals, is determined not to get carried away.
“We know there is still a big game ahead with the semi-final, but we are feeling good and confident,” the Tottenham forward said.
“We just have to go again, keep doing what we are doing and make the country proud.”
Kane added: “So much preparation went into it and I thought we were fantastic today. “It was a difficult game, Sweden made it tough - long balls, different to what we have faced so far.
“We were brilliant at set-pieces, crosses into the box and we are buzzing.”
Goalkeeper Jordan Pickford made some important saves as Sweden rallied in the second half, and felt England had shown a mental strength to progress.
“We knew it was going to be difficult and what they bring to the party, and we managed it very well,” he said.
“It just showed how our ability is coming out and also the mental part of our game.” The Everton number one added:
“We can go and create our own history, but now it is about rest and recovery for the next game. “It is not going to be easy, but we will work hard enough and our ability should show.”