England are now firm favourites to book their first World Cup final spot since 1966.
The Three Lions were comfortable winners over Sweden on Saturday, and they will now face Croatia in their semi-final and England are favourites to win.
Should England win they will face either favourites France, or Belgium – who they met in the group stage.
“We played an opponent who have a clear identity and their collectiveness has been too much at times. After having to give everything emotionally this week, today was a real test,” said Southgate.
“It was a sign of the maturity of this team who are maturing in front of our eyes.
“We’ve got to this point because the collective has been so strong.
“To have gone to the depths emotionally and physically in midweek [against Colombia], and controlled this game and withstood the physical test, was a sign of resilience of a young team who are maturing in front of our eyes.
“But I spoke to the lads and none of us fancied going home. Now we have to be here another week. It’s up to us now which games we play in.”
Bookmakers make France favourites to lift the trophy at 2/1 with Belgium, who saw off Brazil, and England head to head at 11/4 and Croatia priced at 4/1.
The Three Lions are 13/10 to see off the Croatians and bag their second final appearance whilst Croatia are 23/10 to shatter English hearts.
England v France look set to be the finalists at odds of 19/10 to line up a meeting, with a Belgium v England final priced at 12/5.
Aoife Heffron, Spokesperson for BoyleSports commented: “The World Cup quarter-finals was in keeping with the rest of the tournament as it spat out some surprise exits and more penalties. Now Brazil are out of the way France lead the charge as 2/1 favourites but punters can’t get enough of Belgium at 11/4.
“The semi-final match odds suggest an England v France final as both sides go into their clashes as favourites to come out victorious.”