In the middle and late period they tended to view their ancient history with nostalgia and, when things were going badly, envy. Off the top of my head, Attaleiates, Kekaumenos, Anna Komnenos, and others all commented on the reduced state of the Roman empire, but I think that Theodore Metochites says it best in his late 13th century "Lament on the decline of Rome":

"On the one hand, one cannot adequately speak or compose laments on the state of Rome, how badly she has fared until now, and how wretchedly she is doing; on the other hand, it is not possible to remain silent for anyone who has even a moderate ability to feel or to mourn in any way. Alas for that former abundance of good things, the great power and the fame that extended across the world and virtually to all mankind—renown for all things and every kind of virtue and happiness, wisdom, courage, talent, orderliness through full participation in the beautiful; every kind of social grace, on the whole every kind of noble condition, secular affairs governed by human customs, the brilliance suited to a great people and a prosperous society! Most of this is gone, manifestly gone, having gradually disappeared long ago, and degenerates even more from its essence and prime—probably by virtue of the laws of nature, which takes this course in all cases. It has gone down a terrible road, and those who can understand and appreciate what happens fears even more for the future. Indeed, perhaps it would be better for everyone, in order to live without sorrow, not to have understanding, since our lot is to live in this way as successors to those former glories—indeed it would be better if one did not still remember the past, helped by historical accounts, but lived in the present, without knowledge of that great prosperity and glory of our fathers that began a long time ago and continued for many years. However, who could be unaware of such greatness, who is so undiscerning that he cannot infer, from the ancient remains that time continuously stores up, and the lifestyle and conditions that have prevailed until now, that former great fortune, great virtue, and prosperity of every kind?"

And later:

"Therefore, little is left of us after being attacked on all sides, and since we are in such a tight corner insofar as our fortune and our state are concerned, and literally in a very narrow corner of that vast and all-encompassing empire of old, we can only take pride in our ancient reputation."

Keep in mind this was written during a time when the Roman empire really was on its very last legs, being a third the size it was a century earlier, and constantly being reduced in territory on all sides. Writers from earlier centuries, and especially those writing in times of prosperity, tended to be less pessimistic. In good years the Romans could feel a sense of pride and restoration, but in bad years they could easily draw a narrative of consistent decline like many early modern scholars have.