Post-colonial criticism refers to the critique of how literature discusses and relates to the social and political issues brought about by colonialism. Jane Austen's Mansfield Park is actually better recognized as having colonial references, particularly with its references to the slave trade and colony plantations. However, Jane Austen wrote during the time of the Napoleonic wars, a time period in which France was brutally attempting to expand its empire, especially by colonization. During these wars, France fought with Russia, Great Britain, Austria, Portugal, what is now Turkey, and even Naples ("Napoleonic Wars 1799-1815). All throughout her works, subtle references to the Napoleonic wars can be found.
Particularly in Pride and Prejudice, soldiers are encamped in Meryton, where Lydia and Kitty go every day to flirt with the officers. Plus, their aunt Philips frequently entertains the officers. Even Wickham, the antihero of the novel, is an officer. However, while Austen was writing during a time period of obvious tribulation, in Pride and Prejudice she really doesn't discuss anything the military has suffered. Instead, she paints the officers as practically being in Meryton on vacation; they are seen enjoying themselves at every social engagement, including the ball at Netherfield, as we see in the line, "Elizabeth entered the drawing-room at Netherfield and looked in vain for Wickham among the red coats there assembled" (Ch. 18). However, Austen does briefly mention that a private had been flogged in Meryton, which seems to be her way of pointing out the cruel treatment of the lower ranking military personnel, even though she doesn't dwell on the subject (Ch. 12).
Since the only way in which we may see colonization alluded to is through references to the officers, we really can't spend a great deal of time analyzing Pride and Prejudice through post-colonial criticism. The only way in which we would know that the references to the officers are a reference to imperialism or colonialism is if we knew that the officers were presently engaged in the Napoleonic wars. Instead, other books by Austen are better analyzed using post-colonial criticism, such as Mansfield Park and even Persuasion, in which the suffering of the military is mentioned.