The heavily fancied Mannschaft lost 2-1 to Italy in Warsaw following two first-half strikes from Manchester City striker Mario Balotelli.
And the former Fenerbache coach spoke said his side can be proud of their efforts, even if they will not be returning home with the trophy.
"Basically, we have had two very good years," he told ARD. "The team has made excellent progress. We lost once again to a strong Italian team. There is no reason to doubt anything."
Low went on to reveal that there were "tears flowing" in the changing room following his side's exit from Euro 2012.
"In the locker room the tears are flowing. It is as quiet as a mouse in the locker room, no one is saying a word," he added.
"We are very disappointed, but we should not make the mistake of questioning everything. The team played a great tournament."
The 52-year-old coach went on to blame his side's defeat on the defensive errors which provided the Azzurriwith an unassailable two-goal lead, but praised their efforts in the second half.
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He added: "The goals were scored because of mistakes in our defence. But the [team] showed their heart during the second half. Italy were 2-0 in front [at half-time] so it is hard to turn the match around."
Low also explained his decision to hand Bayern Munich midfielder Toni Kroos his first start of the tournament and bring Lukas Podolski and Mario Gomez back into the team.
"With Toni, I wanted to be stronger in the centre, and limit the midfield axis of [Andrea] Pirlo and [Riccardo] Montolivo," he continued.
"Gomez had scored three times [in the tournament so far] and was good in training. Lukas was also good in training. We won in the first few games with Podolski and Gomez."