When considering this question it is important to realise that, when it comes to Roman interactions with early Christians, much of the oppression and persecution that are now synonymous with Romano/Christian relations were propagated and often greatly exaggerated by Christian scholars in both the late Roman Empire and the Medeival period, both as an explanation for the fall of the Empire, and also as a way enhancing the mythology around early Christian figures. Having said this, persecutions of Christians did indeed take place throughout the lifetime of the Roman Empire. To attempt to answer your question, I wouldn't say the Romans ever had to "justify" their persecution of Christians to themselves, the word "justification" suggests that the Romans needed a good reason to persecute Christians, and the reality is that the persecutions were often more of a reactionary and opportunistic endeavour than any concerted effort to suppress the sect, at least until the later, more concerted attempts at suppression that took place under the likes of Valerian in the mid 3rd century AD. The first account we have of Christians being persecuted by the Romans is also one of the most famous: that which took place during the reign of the Emperor Nero in AD64. Both the historian Tacitus, and the more sensationalist writer Suetonius, make reference to the persecution of Christians that took place under Nero following the Great Fire of Rome. Both writers seem to suggest that Nero "shifted" blame for the damage and deaths caused by the fire onto the Christians to deflect attention away from his own poor reaction, as well as allegations that he himself had been involved in the fire's origin. But why were the Christians used, as they often would be, as convenient scapegoats? Both the Bible (17 Acts.18:2) and Suetonius (Claudius, 25) make reference to an expulsion of Jews (which included the Christian subsect) from Rome during the reign of the Emperor Claudius. The Romans were inherently suspicious of any sect that was: A. overly-exclusive and "obstinate"; or B. abnormally ecstatic and indecent, as can been from their suppression of the Cult of Bacchus in 186BCE (see Livy for more information on this). Both Christianity - and wider Judaism - definitely conformed to the former of these conditions, just as much as superstition and misunderstanding contributed to association with the latter. Let us consider these two individually for a moment: As Earle Cairns wrote in his 1996 book "Christ Through the Centuries" 'the exclusive sovereignty of Christ clashed with the Emperor's claim to his own exclusive sovereignty'. In essence, the monotheistic faith followed by Jews, and by extension Christians, required devoted and unquestioning loyalty to God and/or Christ and would brook no deviation or acceptance of other religions. The Romans treated religion as a tool as much as a faith and often mixed their own gods and deities with those of the peoples they conquered to ease the transition to Roman rule (plentiful evidence of this can be found in the Roman occupation of Britain where many local gods were presented as aspects of Roman deities) but Christianity and Judaism would not accept this, just as they refused to accept the primacy of the Roman Emperor which, to the Romans, was as good as openly rejecting Roman rule. The obstinacy of Christians in this regard was so great that Pliny the Younger and the Emperor Trajan discussed in their correspondence how one might root out Christians in the eastern half of the Empire by forcing a group of suspects to swear an oath on the Emperor - Christian's faith would prevent them from doing so and make them instantly conspicuous. This obstinacy was anathema to the Romans and contributed to their mistrust and suspicion of all things Christian. Similarly, misunderstanding and superstition led to an increasingly hostile Roman perception of Christianity, where they were usually tolerant of various religions. The early Christian practice of holding gatherings and services in the home, rather than in a temple or other place of worship, contributed to misunderstanding, whereby Christians were accused of partaking in such illicit acts incest and cannibalism (many historians have suggested this to be a corruption of the Body and Blood metaphor and the Christian practice of referring to one another as "brother" and "sister").

Thus, we can see WHY Romans were predisposed to suspecting Christians and thus why they were such a convenient scapegoat for the likes of Nero to pin blame on when required. Christianity, at least in its early stages, was completely alien to the Roman way of thinking. It was, like it's Jewish predecessor, resolutely monotheistic and its followers obstinately loyal to their God. Romans did not have to justify the persecution of Christians, to themselves or to anyone else, Christianity was a convenient community on which to appropriate blame.