"We have already made several pieces of history. [The] biggest win in the tournament for England, first knockout win in ten years, first quarter-final win for longer, so we are just looking to keep breaking those barriers down," Southgate told journalists.
He added that the team was "really proud with the style we played, with the intelligence that we have performed under pressure."
Meanwhile, England midfielder Jordan Henderson stated that England are focused on their semi-final match against Croatia and not on the legacy of the English football.
"I think we should concentrate on what we want to do, on what we want to create… It's a massive game for us, but there's no need to make it bigger than what it already is. We're gonna obviously take a lot of good things in the past in terms of 1966 and what we achieved then, but it was a long time ago, so not too many of us can remember that," Henderson said.
The UK Embassy in Moscow said on Tuesday that the UK officials were willing to help England fans who had arrived in Moscow to support their team in Wednesday's World Cup semi-final encounter against Croatia.
"The Foreign Office team is in Moscow where England take on Croatia in the #WorldCup semi-final. We’ll be in locations around the city ready to meet England fans," the embassy posted on their official Twitter account, adding a telephone number that "UK nationals requiring consular assistance" could call.
The Three Lions went on to beat Colombia on penalties in the last 16 before outclassing Sweden 2-0 in their first quarter-final appearance since 2006.
England will next take on Croatia in their first semi-final since 1990 at Moscow's Luzhniki Stadium on Wednesday.