So, I can't speak about 'Late' Latin (late 2nd century-5th century), but I can speak about what was called Silver Age Latin (approx. A.D. 14 - 138, per Wheelock's Latin). My senior undergrad thesis was on the satires of a fellow named Aulus Persius Flaccus, who wrote excellent satire (while Nero was emperor) which absolutely ripped what he saw as the absurd excesses of the time:

"These poems paint a world which has bottomed out...with the poet insisting from the start that his brand of didactic has no audience and satire does no good. His world is fake, soulless, and rotten to the core, and that rottenness...comes from the top down." -Kirk Freudenberg, Satires of Rome [an excellent book, by the way - one section just after this is called 'Faking It in Nero's Orgasmotron']

A sample of Persius' poetry for you:

Si quid turbida Roma / elevet, accedas examenve improbum in illa / castiges trutina nec te quaesivieris extra.

If scatter-brained Rome should weigh something up and find it too light, you shouldn't join in (the general disdain) or attempt to adjust the balance on a morally-corrupt scale like that! No, you shouldn't look to find yourself anywhere out there! (Translation by Freudenberg)

And another great passage about an overly fat upper-class male, who has stuffed his face in the baths for the last time:

sed tremor inter uina subit calidumque trientem
excutit e manibus, dentes crepuere retecti, uncta cadunt laxis tunc pulmentaria labris.

"But as he drinks, his throat emitting long noxious Belches, a sudden tremor makes the warm glass slip from His hand, his bared teeth chatter, and the greasy food slides From his slack mouth."

The guy is in the baths in the midst of stuffing his face - and then he croaks! Delightful.

So, many Romans were aware that a sort of decline was occurring. In Persius' case, they highlighted it by ripping into it via satire and similar invective. As for later on, I cannot answer that question, but during Persius' period (A.D. 34-A.D. 62), satire was the primary means to criticize while still contending with the power of the emperors.

edit: a bit more clarity

As someone else mentioned, in the centuries following the "fall" of Rome (or at least what survives today) artists focused nearly entirely on Christian themes, rather than the world around them. One notable exception are portraits of powerful people in the Byzantine empire, but that doesn't really relate to the city of Rome itself. I did a bit of work in graduate school on the state of Roman housing in the 6th, 7th, and 8th centuries. There are written accounts of farmers bringing their animals to graze in the forum because it was basically an overgrown field by that point, which was a stark contrast to the bustling area it was at the height of Rome's population. I also read several articles on archaeology done in Rome that was relevant to the later period, which basically showed people reusing and subdividing existing homes. The infrastructure and wealth for new building wasn't typically available in Rome, so the people that still lived there used what materials they had access to to modify existing structures. My advisor was firmly convinced that some apartment buildings in use today date to the Roman empire and had been maintained, modified, and occupied continuously since then.

I'm not sure of anything that fits your question completely, but there is a guidebook to the sights of Rome from the 12th century called the Miribilia Urbis Romae. This was far from Rome's nadir, but it was still significantly smaller and simpler than it had been at the height of the empire. The book was written at a time when the people of Rome were looking to the traditions of the past as a way to gain independence from lord-popes by establishing a republic again. This means that the decline of Rome was of no interest to the writer. He wanted Rome to seem great from beginning to end. What is does show is how the medieval Romans perceived the ancient ruins around them. Many ruins were misidentified (The tomb of Caelius Rufus is misidentified as the tomb of Remus for example) or were associated with stories from the Christian era (there is a story that Augustus received a vision of Christ at the time Christ was born). Altogether it shows an alienation from the ancient past and presentism (projecting your present situation onto the past).

On the other end are late antique writers who comment on Rome during the period when the population was crashing. The Life of Melania (5th c.) follows a very (I mean Scrooge McDuck levels) wealthy woman as she flees Rome in the face of the Visigothic invasion to lead an ascetic life in the Holy Land. This shows that people with the means to leave Rome did, and we can extrapolate that the city lost a large part of its aristocratic economic and social base in the face of invasions. In contrast, Rutulius wrote a poem praising the city's greatness just three years after being sacked by the Visigoths (i.e. AD 413). It's safe to say that Rutilius was in denial.

Unfortunately, I'm not familiar with the period between these two, but there were many flourishing writers. I would assume that Gregory the Great (pope from 540-601) would have something to say about it in his corpus.

Where are your population figures from?

Wasn't this a theme for art of a certain period (around the 17th Century) with landscapes featuring rural scenes amongst bits of Roman ruins? I kind of thought of Poussin, but a quick review didn't find the works I was thinking of, any suggestions? Yes, a millennia after the fall of Rome but very evocative art.

As a followup question, I would be interested to know if any modern examples exist of cities in such extreme decline in population, as possible comparisons/contrasts to the OP's question about Rome.

The museum of the trajan market and the crypt of Balbus share some illustrations of the evolution of Rome, a part of it is present in the guide of the museum, here are four evocations of the cryta balbi through the late antiquity and the middle ages: http://antiikki.taivaansusi.net/CryptaBalbi4.jpg