Andre Schurrle and Mesut Ozil scored in the additional 30 minutes for the pre-game favorites, ensuring that Abdelmoumene Djabou's goal in the dying seconds was just a consolation after a battling display from the North Africans.
Low was disappointed that makeshift center back pairing of Per Mertesacker and Jerome Boateng were exposed by Algeria's long passes from deep and admitted his frustration at his side's poor opening period on the whole.
"It was a victory achieved by our strength of will," he told ZDF. "But the first half was bad. During the second half and extra time we were the better team and had the better chances. We should have decided it during the second half.
"We gave away an awful lot of passes. This was unusual. And we had problems in getting behind their defenders.
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"We had to switch our lineup again as Mats Hummels was not fit to play. Per Mertesacker and Jerome Boateng have played together many times and they know each other - normally they are very good. But Algeria played these long balls very well, they are very good at that.
"In a match like this you have to see how it develops. We need players we can bring into that match and who can make the difference. Today we brought in Sami Khedira and Andre Schurrle and they provided us with a boost.
Manuel Neuer essentially played as a makeshift sweeper throughout the last-16 tie in Porto Alegre and came to the side's rescue on a number of occasions when Algeria broke through the Germany back four, but the goalkeeper insisted his performance was nothing unusual.
"I played no different to how I usually play at Bayern Munich or in the national team," he said. "The pitch was wet and that made it a little easier for me."
Germany will face France on Friday and, if it wins that last-eight match, it will come up against Brazil or Colombia in the semifinals.