It was a different game from then on, with Croatia suddenly playing with accuracy and objective as England lost their shape and composure, though Kane missed a chance to win it in stoppage time when he headed wide from a free kick.
Croatia started the find their range as the second half wore on and Perisic levelled for Croatia in the 68th minute, nipping ahead of Kyle Walker to steer home Sime Vrsaljko's cross past a diving Jordan Pickford.
Despite England's exit, Southgate remains proud of the impact that his players have made.
"I think in the first half we were really good and maybe we could have got another goal", Southgate told ITV. The whole thing is beyond where we thought we might go.
Its previous two games went to extra time and then emotionally draining penalty shootouts. "Second half, fair play to Croatia they came out and put the pressure on and we were under the cosh for a little while", the 24-year-old skipper said.
They will take on favourites France at 1am Monday morning Australian eastern time, while Belgium play England at midnight on Saturday night in the third placed playoff.
He said: "All these words from them we take, we were reading and we were saying: 'OK, today we will see who will be exhausted.' They should be more humble and respect their opponents more".
However, this time he was far more direct, playing on the last shoulder of the Croatian backline and zooming off towards goal rather than retreating away from it.
Loud cheers rang out after each goal, fans waved the red, white and blue national flag, and after the final whistle Croatian TV showed wild celebrations breaking out in towns and cities.
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