The 52-year-old trainer is worried by his side's inability to take their chances, but Mario Gotze was impressed by the minnows' resolute performance
The hosts dominated proceedings throughout in Hannover, but could only muster up three goals, with Miroslav Klose, Thomas Muller and Marco Reus all guilty of squandering chances.
It was a familiar story for Low's side, who were uncharacteristically wasteful in front of goal in their recent defeats to Argentina and Italy, and the 52-year-old is adamant that his troops must improve.
"I know that it was our biggest victory ever against the Faroes, but I think we have to be criticised here because we had many chances, but not enough goals," he told reporters after the match.
"In some situations we could do better. We sometimes don't do the little things correctly. Faroe Islands are not the benchmark against which we measure our other opponents in the group."
Mesut Ozil, who scored two excellent second-half goals to put the visitors to bed, agreed with his coach's criticism, but stressed that his team-mates gave their all.
"We put pressure on them from the start and we wanted to get an early goal, and we had many scoring chances in the first half," said the Real Madrid man.
"We gave everything, we deserved to win and can be satisfied with our result. We have taken the first step."
Mario Gotze, who netted the other goal to get the ball rolling, meanwhile, has saluted the Faroes' resolute performance in the face of adversity.
"They stood very deep, and it was difficult to break through them. We should have done better in one or two situations, but we did well for the goals," he said.
Germany continue their qualifying campaign against Austria on Tuesday September 11.