The 53-year-old celebrates an undefeated qualifying campaign as the Bavarians booked their ticked to Brazil 2014
Sami Khedira, Andre Schurrle and Mesut Ozil were on target to ensure their nation remained unbeaten in Group C and book their ticket to Brazil with one game to spare.
Low praised his troops for their performances, but knows there are areas Germany must improve on if they are to win the 2014 World Cup.
“Overall it was a very good qualification. We won eight out of nine games and the ninth should have been a win, too,” he told reporters. “So we can be satisfied.
“The team did their duty. Against Ireland we stayed patient and created chances at the right times.
“After the break we had some minutes where we were too relaxed and we did not look good in two or three situations.
“Little things must improve and I see two points: We have to be more stable defensively and play better in the final third.”
Captain Philipp Lahm, meanwhile, is delighted to have seen his side's hard work pay off following 12 months of hard work.
“The team worked well for over a year. There were good and less good matches, but this is normal," he added.
“Against Ireland we built up pressure right from the beginning and conceded only few chances.
“We knew the Irish would give their all and never give up. The early lead was important.”
Schurrle has saluted his side's patience in attack against Noel King's side.
“We were prepared well for that match,” Schurrle told reporters. “We were patient, looked for spaces, scored three goals and won deservedly. Ahead of my goal, Toni Kroos played it perfectly."
Finally, Thomas Muller added: “It was a little exhausting. Our opponent fought a lot and stood almost the entire tire time around the penalty box.
"I can’t blame them for doing that and it is our task to find solutions for that. We did so pretty well.”