Sabella's side fell behind for the first time in the tournament when Mario Gotze scored with seven minutes of the extra 30 to play in Rio de Janeiro, and there was no way back.
The Argentines had chances - Gonzalo Higuain, Lionel Messi and Rodrigo Palacio all missing clear ones - and Sabella conceded his side "lacked a bit of efficiency".
But he said: "The players were warriors. They left their skin on the pitch. They did everything.
"The team have played an extraordinary World Cup. The players can look at each other and say they gave everything."
Argentina had one fewer day to prepare for the final and were taken to penalties by the Netherlands in the last four.
Sabella said: "Taking into account who the opponent was and that we had one less rest day, this was our best performance.
"We played a day later and extra time and the only thing I can do is congratulate my players and also congratulate Germany."
Sabella's agent reportedly said in the days before the final that his client would leave his role as manager no matter what the outcome.
He did not confirm that immediately after the game, saying: "What I want to do is be with everyone in the group. I need to rest."
Sabella also backed the decision to award the Golden Ball - given to the tournament's best player - to Lionel Messi, who did not score in the knockout stage.
"Messi is always one of the greats," he said. "He deserved the award."
Javier Mascherano, Argentina's man-of-the-match in the semi-final and again impressive in the Maracana, said: "The pain is immense. We wanted to win this for the people of Argentina, for those who came here to support us, but we lost.
"We have represented our country the best we could though. We have to lift our heads despite the pain. We gave everything we could out there.
"We had the best chances but we didn't take them. And we only had to last another five minutes at the end. We just didn't have that little bit of luck that you need in a final."