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Despite the loss, the Australian team still qualifies for the competition’s knockout quarter-finals in November.
“The goal was to qualify here and the boys did extremely well this week,” Australia captain Lleyton Hewitt said. “I’m really proud of all the guys and the whole team.
"They prepared and did everything they needed to get the result we were after and we’ve given ourselves a chance, which is what we came here to do. It’s nice to be through to the quarters.”
Jan-Lennard Struff gave Germany a perfect start in the tie, striking 23 winners to six in a 6-1 7-5 victory against Max Purcell in his Davis Cup singles debut.
Thanasi Kokkinakis then levelled the tie with a 7-6(6) 6-1 win against Oscar Otte, with 12 aces helping the Australian in the one-hour and 43-minute encounter.
“I’m happy I could get a win for the team,” said Kokkinakis, who was contesting his first match for the week after overcoming illness.
German pair Tim Puetz and Kevin Krawietz sealed victory for Germany, for the third time this week, in the deciding doubles rubber. The duo maintained their unbeaten Davis Cup records with a 6-4 6-4 win against Wimbledon champions Matt Ebden and Purcell.
The Australian team is one of eight nations advancing to the knock-out stage of this year’s Davis Cup competition.
Hewitt's men will face Netherlands, the winner of Group D, in a must-win quarterfinal on 23 November in Malaga.
“Any match is going to be extremely tough, and they obviously came through their group with flying colours,” Hewitt said. “So, we’ll have our work cut out, but we’ll prepare as well as possible.
"It will be a massive goal for our guys to be playing well come middle of November.”