The three-time champions ended their campaign with a 3-2 victory over Uruguay in the third-place play-off in Port Elizabeth on Saturday night.
Youngster Thomas Muller grabbed his fifth goal of the tournament when he opened the scoring.
Edinson Cavani equalised for Uruguay, before Diego Forlan volleyed the South Americans in front after a goalkeeping error allowed Marcell Jansen to equalise.
A thrilling game — the most open contest of the World Cup — was finally decided when Sami Khedira headed home to give Germany their second third-place finish in consecutive tournaments.
Löw said: “In the second half, when we were forced to dig deep, we saw the mental strength the team had to resist and then snatch victory.
“I’m pleased with that, the team deserves it.
“Altogether, what we’ve achieved, we never would have expected it eight or nine months ago.’’
The result was made even more remarkable for Löw, who was without leading strikers Miroslav Klose and Lukas Podolski and captain Philipp Lahm.
Uruguay coach Oscar Tabarez paid tribute to his side, who were the last team to qualify for the World Cup and among the last to leave it.
“Uruguay have been one of the surprises of the tournament and we still don’t realise what’s happened back home,” Tabarez said.
“I received an email on Friday from a lady I didn’t know who said, ‘Thank you, thank you, thank you for having changed the image of our country’.
“I’m surprised, it’s the beauty of sport and the serious work we’ve accomplished.”
Tabarez’s team were one of the least likely of the South American teams to make any major impact in South Africa, but the coach was pleased with the display in their final game.
He added: “The match was contested by two teams who really wanted to finish in third place, by two teams who gave everything.
“We made one mistake too many, but we showed that we were capable. We showed that we could compete with any team in the world.”
URUGUAY: Muslera, Fucile, Lugano, Godin, Caceres, Maxi Pereira, Perez (Gargano 77), Arevalo Rios, Cavani (Abreu 89), Suarez, Forlan.
GERMANY: Butt, Boateng, Friedrich, Mertesacker, Aogo, Khedira, Schweinsteiger, Muller, Ozil (Tasci 90), Jansen (Kroos 81), Cacau (Kiessling 73).
Referee: Benito Archundia Tellez (Mexico).