"I am sorry, but the flight is full."
Translation:Jeg er ked af det, men flyet er fuldt.
'undskyld' = excuse me. (Undskyld, må jeg se den? Excuse me, may I see it?).
In this DL-sentence "I'm sorry but ... " should be translated into "Jeg beklager, men ..." You can use the term "Jeg er ked af det", if you are sad or apologizing for something, which might be the case here, but I doubt it. (I'm Danish)