Well, I think you have to accept that concentration compactness is *concept* rather than a *result*. The intro of the mentioned book starts with 

> The subject of this book, concentration compactness, is a method for establishing convergence, in functional spaces, of sequences that are not a priori located in a compact set.

If you accept that there is no theorem that captures the concept and don't want a whole book, you should read the explanation on concentration compactness [here][1] (longer than a theorem, but shorter than a book).



  [1]: https://terrytao.wordpress.com/2008/11/05/concentration-compactness-and-the-profile-decomposition/