Except his German guards, who remained loyal. If I remember right, wasn't the situation somewhat fraught immediately after his death? That would indicate there were still plenty of 'Caligulists' at large.
Blood-thirstiness is a complex subject. To some extent, people are sheep. If powerful leaders tell them to be blood-thirsty and give them absoltuion or an excuse, be it religious, racial, or political in nature, then they follow suit and rationalise what they've done even if they have lingering doubts and guilt. As individuals, without a group to hide behind, most people cannot behave in that manner (and fewer still would contemplate it).
In other words, as social animals human beings run with the crowd.
Regarding leaders, we tend to study them in siolation or in relations to their immediate associates such as family or allies. However, in an organised situation you do often find able organisers that exist in the shadows. For the most part these faceless assistants are of no great account in history (or we'd know who they were) but their influence cannot be underestimated. Augustus for instance was a typically cautious leader (one reason for his popularity - the Romans liked cautious leaders) and despite the peace and prosperity of his reign, doesn't seem to show any great flair in civic management. Granted, he did some clever things. He kept Cleopatra at arms length (what a dodgy woman she was!), reinvented the Roman legions as 'soldiers', not 'brothers', "Found Rome in brick and left it in marble", and certaibnly staged a lot of games. And so forth.
But his real success was to do as little as possible. Roman emperors who were remembered fondly often share that characteristic. By maintaining as much of the status quo as possible, fewer influential people got upset. Augustus in fact walked a tightrope in his early days (and due credit to him) and his title of Princeps demonstrates that. Yes, Agustus is in charge, but not an ego maniac like Caesar or those horrible kings we once had. In other words, he was a dictator who pretended he wasn't. You could in fact argue, as I have, that he did little more than bribe the Roman public to keep him in power, though there are are indications he kept an eye out for possible up-and-coming rivals and dealt with them in pretty much the same manner as any modern gangster might.
Now the state had to continue running. We know that Emperors struggled mightily to run it in later years, the empire was just too big for one man to control, so the ability and integrity of most bureaucrats who worked on Augustus's behalf must therefore have been somewhat better than in later reigns. They were opening up a genre of government, they had the full support of the Princeps, and had every reason to demonstrate skill and endeavour.
Later bureaucrats simply wanted a bit of status, a sinecure, and a source of income, and backscratched their way into an existing role. Some might argue that Augustus kept a close enough scrutiny to ensure his own men were doing a good job. I have to concede that possibility. In a sense, he may have been an able administrator - I would argue he was an able manager.
Status and income are universal legitimate demands from any human for any government; the real success of the Augustus' administration (on a global all-time scale) was ensuring plenty of them to millions of Roman citizens for centuries; such kind of "bribing" is what the human "sheep" might reasonably expect from the real top world leaders.
Their civic management was enough to explain why the Republic never came back, even after Chaerea butchered Caius; in fact, even among the most noble senatorial families, most of them were more comfortable as bureaucrats (some of them even efficient) under a strong regime than as petty lords under the chaos of civil war.