The Germans take on Algeria in Porto Alegre for a place in the quarter-finals against either France or Nigeria next Friday.
Algerians have "not forgotten" that they have a World Cup score to settle with the Germans, according to coach Vahid Halilhodzic.
Algeria were controversially eliminated from the 1982 World Cup on goal difference when West Germany – whom the Algerians had beaten 2-1 in their group game – and Austria played out a mutually beneficial 1-0 win for the Germans.
"We have not forgotten about it. Everyone talks about Algeria and Germany from 1982," Halilhodzic has said.
The 1982 match was dubbed 'the game of shame', but Löw rejected any talk of their Brazil 2014 clash being a revenge mission for the current Algeria team.
"Why should players who weren't even born then want revenge? I can't understand that," said the German coach.
His sentiments were echoed by German Football Association (DFB) president Wolfgang Niersbach.
"Terms such as vengeance or revenge are not appropriate after so many years," he said.
With the subject closed, Löw prefered to focus on the 'magic' of the knock-out phase with the Germans chasing a fourth World Cup title.
"Our team is on fire, we're going into the game with a lot of confidence," Löw said.
"Games like these have a certain magic and tension, there is no second chance.
"Concentration is the order of the day, Germany has always been a tournament team and I trust the quality of this team."
Löw is all too aware that the expectations of a fourth World Cup title are growing back home in Germany, but he warned against looking past Group H
"Anyone who things that an easy opponent is waiting for us in the next round is making an enormous mistake," said Löw, after Germany finished as Group G winners.
Algeria are a "compact, hard-running and aggressive team," and the euphoria of reaching the knock-out stages in huge in the north African state, acknowledged Löw.