The underdogs had upset Bayern Munich, Borussia Monchengladbach and Eintracht Frankfurt to make the DFB-Pokal semis.
But their hopes of reaching the final were dashed by second-half goals from Marlon Ritter and Almamy Toure.
It is the first time Kaiserslautern have reached the final since 2003, when they lost to Bayern Munich.
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