The use of the word critique presents some problems. The word was first used in English as an alternative spelling of the noun 'critic' (or 'critick', as it was sometimes written) in the early 18th century. It usually meant 'criticism', or 'review'. Currently it appears to have a slightly different meaning from 'criticism' - although not all writers make a clear distinction.
A critique tends to be a more structured, a more reasoned critical account than an 'ordinary' criticism. A scholar may prepare a critique of a given theory which could be of book length. (Such a critique may well be the first appearance of the beginning of a new theory.) The word 'structured' is often used to describe a critique, as opposed to a criticism.
In American English, the verb 'to critique' (~ to make a critique of) exists. AWE's view is that it is unnecessary. Don't use it. (Above all, do not use it in the sense '
to make a negative criticism of'.)