Miroslav Klose struck the winner in the 14th minute to condemn the Royal Blues to their straight defeat.
Slomka now takes his side to Porto on Wednesday for the second leg of their Champions League second-round clash knowing another loss could cost him his job.
Copyright (c) PA Sport 2008, All Rights Reserved.
Do YOU want to write for GiveMeSport? Get started today by signing-up and submitting an article HERE: http://gms.to/writeforgms