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 (longer than a theorem, but shorter than a book).