After a goalless first forty-five minutes Hoffenheim took the lead five minutes after the break through Christoph Janker.
Rovers drew level just past the hour mark with a Benni McCarthy goal but the German side regained the lead just two minutes later when Jaissle gave them a 2-1 lead.
Janker added a third for Hoffnheim just moments before the final whistle.
Rovers Beaten n Austria
Rovers 1st half: Friedel, Reid, Ooijer, Nelsen, Warnock, Derbyshire, Emerton, Pedersen (Judge 34), Treacy, Roberts, Santa Cruz.
Rovers 2nd half: Brown, Kane, Nelsen, Warnock, Olsson, Judge (Hodge 75), Tugay, Mokoena, Gallagher (Peter 75), Fowler, McCarthy.