But there was no doubt of the players' place in the affections of the nation, as illustrated by the fans who remained in the stadium in Moscow long after the final whistle to serenade the team.
With the whole of England finally daring to believe, the 2-1 loss against Croatia came as a devastating blow to fans up and down the country.
In a moment captured by cameras, Southgate - a former player himself who ended up managing the English national team for his first World Cup this year - shared a tender embrace with his wife, Alison, in the empty stands.
England captain Harry Kane will likely come home from the Fifa World Cup with the Golden Boot as the tournament's top scorer and a burnished reputation as a feared forward.
Even before his goal, Mandzukic had spent some minutes on the turf after a collision with England goalkeeper Jordan Pickford and an agonising attack of cramp left him once again prone on the pitch in the wake of his decisive strike.
"We were like lions out there tonight and we will be the same in the final", he said.
But even though England are out, they've still had an awesome tournament.
I said this in the group stages and I'm thinking, quarter-finals England will get knocked out.
In Moscow, Croatia fans said they were taken aback by their side's win.
"Whether that had an effect on us not wanting to take as many chances as we had, subconsciously, I don't know". I don't know of a smaller country in a World Cup final. Thank you, England": "A simple message of gratitude from the Express, accompanied by a picture of Southgate and his players showing their appreciation to the travelling supporters.
"I'm sure we lacked in some areas, there are things we could've done better. It's going to hurt for a while, of course, but we can hold our heads up high".