More natural to just say "sorry for the inconvenience". If you want to use the word caused, it's best to say: "sorry for the inconvenience it caused" or "sorry for the inconvenience I caused".

There are numerous ways of writing this: "Owing to a signal failure at Three Bridges, services are severely delayed." could be followed by any of: 1 We are sorry. 2 We are sorry for the inconvenience. 3 We are sorry for the inconvenience caused. 4 We are sorry for the inconvenience this has caused. 5 We are sorry for the inconvenience caused by this. 1 and 2 are too abrupt. 3 and 4 are typical, 5 is too wordy. So, Niwantha, yes: form 3 is the result of contracting the sentence, removing an unnecessary reference to 'this' which is obvious from the context. Your example (lack of preparation) doesn't quite work - the lack of preparation needs to have been mentioned already for the contraction to work.

I would add the point that "caused" means: it could have been avoided, that something is to blame. Sorry for the inconvenience might be said about weather at an airport to the customers whose flights got cancelled (the airlines can't control the weather); A waiter spilling a drink on a customer because someone bumped into him (it isn't exactly his fault or the other who bumped him). In these examples sorry for the inconvenience is understood to have (it caused) as part but not needed to be said. Adding "caused" should only be used when to make a more elaborate apology for example: "sorry for the inconvenience caused by the lack of preparation".