Luis Aragones' side claimed their first silverware since 1964 courtesy of Fernando Torres' clever first half finish.
Low's primary goal was to follow in the path of Bertie Vogts, who steered Germany to the Euro 1996 crown, but Low feels that even in defeat reaching the final deserves praise.
And he had nothing but compliments for his players, as he sets about helping them to qualify for the World Cup in two years' time.
"I have to compliment the team for what they have achieved over the past few weeks," said the 48-year-old.
"It has been fantastic. The players are obviously disappointed, but they have every reason to hold their heads up high."