Goals from Per Mertesacker in the first half and Mesut Ozil and Thomas Muller in the second handed the Germans a routine FIFA World Cup qualifying win on Tuesday.
Their hosts finished the game with 10 men following Atli Gregersen's dismissal 15 minutes from time for the foul that led to Ozil's goal from the penalty spot.
The result leaves Germany five points clear of Sweden at the top of group C with just two games remaining.
And Low admitted that the performance was of secondary importance to the result.
"It was a mandatory requirement to pick up three points here," he said.
"It was the sort of game we had expected. They stood with 10 men in the penalty area, they are a team who know how to defend well."
Germany dominated possession throughout the match as the Faroe Islands, ranked 175th in the world, struggled to make any impression on the German defence.
But Low felt there was room for improvement from his side.
"If there is anything to criticise, we have to work on our final touch," he said.
"We didn't move as well after the break as we had in the first half and we have to improve our game in the final third of the pitch."
