What we find when we look at Roman history over all is that the Romans have been more brutal to themselves in their own Civil Wars (especially those before the time of Christ) than anything suffered under the worst of the barbarians--either the current Goths or the ancient Gauls. After all, it was the war between Marius and Sulla which led to that between Caesar and Pompey, which led to that between Octavian and Anthony, the last two sets of which destroyed the Republic completely.
Given all the tragedies that befell the Roman Republic, which died before the time of Christ, how can the Romans logically blame the Christians for the current tragedy? The pagan gods did nothing to stop those earlier calamities, so it can't be a matter of them having abandoned Rome because it has turned to Christ. Something else must be at work in the world.