Romans had always held "barbarians" in contempt, and they believed that the lands held by barbarians (such as Scotland and Germany) were largely unsuitable for civilization, being too cold and wet for the kind of Mediterranean agriculture Romans were accustomed to. Romans believed that barbarian peoples like the Germans were inferior to subject peoples like the Celts, who could at least be made useful subjects (and, later, citizens) of the Empire. For the entire history of the Empire, the Romans never seem to have figured out exactly which groups they were interacting with; they would simply lump them together as “Goths” or even “Scythians,” a blanket term referring to steppe peoples. Occasionally, hundreds of years after they “should have known better,” Roman writers would actually refer to Germans as Celts.
It is easy to overstate this attitude; there were many members of German tribes who did rise to prominence in Rome (one, Stilicho, was one of the greatest Roman generals in the late Empire, and he was half Vandal by birth!). Likewise, it is clear from archaeology that many Germans made a career of fighting in the Roman armies and then returning to their native areas, and that many Germans looked up to Rome as a model of civilization to be emulated, not some kind of permanent enemy. Some Romans clearly did admire things about certain barbarian groups, as well - the great Roman historian Tacitus, in his Germania, even praised the Germans for their vigor and honor, although he did so in order to contrast the Germans with what he regarded as his own corrupt and immoral Roman society.
That said, it is clear that the overall pattern of contact between Rome and Germania was a combination of peaceful coexistence punctuated by many occasions of extreme violence. Various tribes would raid Roman lands, usually resulting in brutal Roman reprisals. As the centuries went on, Rome came increasingly to rely on both barbarian troops and on playing allied tribes off against hostile ones. In fact, by the late fourth century CE, many (sometimes even most) soldiers in “Roman” armies in the western half of the Empire were recruited from barbarian groups.
The only place worthy of Roman recognition as another "true" civilization was Persia. When Rome was forced to cede territory to Persia in 363 CE after a series of military defeats, Roman writers were aghast because the loss of territory represented “abandoning” it to the other civilization and state. When barbarians seized territory, however, it rarely warranted any mention among Roman writers, since it was assumed that the territory could and would be reclaimed whenever it was convenient for Rome.
Meanwhile, there had been hundreds of years of on-again, off-again ongoing wars along the Roman borders before the “fall” of Rome actually occurred. Especially since the third century, major conflicts were an ongoing reality of the enormous borders along the Rhine and Danube; those conflicts had prompted emperors to build the system of limes that held the barbarians in check. From that point on, the majority of Roman legions were usually deployed along the limes, the semi-fortified northern borders of the Empire. There is evidence that many of those soldiers spent their careers as not-so-glorified border guards and administrators and never experienced battle itself; there is no question that the performance of the Roman military was far poorer in the late imperial period than it had been, for instance, under the Republic.
In turn, many of the barbarians who settled along those borders were known as federatii, tribal groups who entered into treaties with Rome that required them to pay taxes in kind (i.e. in crops, animals, and other forms of wealth rather than currency) and send troops to aid Roman conquests, and who received peace and recognition (and usually annual gifts) in return. The problem for Rome was that most Germanic peoples regarded treaties as being something that only lasted as long as the emperor who had authorized the treaty lived; on his death, there would often be an incursion since the old peace terms no longer held. The first task new emperors had to attend to was often suppressing the latest invasion from the north. One example was the Goths, settled at the time somewhere around present-day Romania, whom Constantine severely punished after they turned on his forces during his war of conquest leading up to 312 CE.
The bottom line is that, as of the late fourth century CE, it seemed like “business as usual” to most political and military elites in the Roman Empire. The borders were teeming with barbarians, but they had always been teeming with barbarians. Rome traded with them, enlisted them as soldiers, and fought them off or punished them as Roman leaders thought it necessary. No one in Rome seemed to think that this state of affairs would ever change. What contemporary historians have determined, however, is that things had changed: there were more barbarians than ever before, they were better-organized, and they were capable of defeating large Roman forces. What followed was a kind of "barbarian domino effect" that ultimately broke the western Empire into pieces and ended Roman power over it.
One other factor in the collapse of the western half of the Empire should be emphasized: once Rome began to lose large territories in the west, tax revenues shrunk to a fraction of what they had been. While the east remained intact, with taxes going to pay for a robust military which successfully defended Roman sovereignty, Roman armies in the west were under-funded, under-manned, and vulnerable. There was thus a vicious cycle of lost land, lost revenue, and poor military performance that saw Roman power simply disintegrate over the course of less than a century. Even the handful of effective emperors and generals in the west during that period could not staunch the tide of defeat.