Rangnick’s men had emerged as potential dark horses after topping a group containing France and the Netherlands.

But they were undone by their set-piece defending in the last 16 tie as Turkey defender Merih Demiral scored twice in Leipzig.

Michael Gregoritsch quickly pulled a goal back for Austria and only a stunning save from Mert Gunok denied Christoph Baumgartner a dramatic equaliser deep into stoppage-time.

“We didn’t have the necessary luck,” said the former Manchester United coach.

“I believe if the game had gone into extra-time we would have won the game because the Turkish team were exhausted and we had a physical advantage.”

Austria scored seven goals in their four games at the tournament — more than England, France and Portugal, who have all advanced into the last eight.

“I think the four games we played were very entertaining, including today’s game,” added Rangnick.

“Not everything went as accurately as we want. We could’ve played a few passes better but four very entertaining, intense games.

“I’ve seen other games when it was difficult to even stay awake and that was not the case in our games.”

Turkey will face the Netherlands in the last eight in Berlin on Saturday.