The goalkeeper was alert on a handful of occasions against les Bleus, pulling off a diving stop to deny Mathieu Valbuena and a one-handed save against Karim Benzema at the death.
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"We gave everything for 90 minutes," Boateng told ARD. "France was a strong opponent, but we fought in a great manner. And Neuer is a fantastic keeper.
"You can't stop France for the whole 90 minutes, but we did a great job. Now we want to improve further."
Fellow defender Philipp Lahm anticipated a close match but was delighted with the efforts of his team-mates as they overcame their European counterparts.
"It was not easy, but we fought as a team. Two good teams fought against each other, that is why it was 50 per cent," the captain said.
"It is a World Cup quarter-final, so you can not let the opponent have any chances. It was important that we scored the first goal."
Neuer himself relished the opportunity to face les Bleus at the Maracana and is now looking forward to the prospect of a last-four encounter with either Brazil or Colombia.
"It was amazing to play in this stadium against France. We played nice football and now we are in the semi-final," he added.