The thing is that the majority of the Ukrainian military, police, internal troops and other law enforcement were against those neo-nazi revolutionaries who disposed the president. What they wanted from the president when he was still in power was to give them permission to use more real force and weapons against the opposition. Yanukovich enjoyed full loyalty of the troops, at all levels, from top to the very bottom. It was only his cowardry and the pressure from the West that kept him from ordering suppression of the revolt.
Consequently, after the president was overthrown, the former rebels started mass scale actions aimed at the humiliation of the troops. In western cities the soldiers were forced to stay at their knees and ask for pardon and were beaten. In some cases the nazi militias even humiliated the traffic police while taking videos of these actions. Consequently, some most loyal and disciplined troops such as special forces "Berkut" were disbanded by the new government without keeping their rank, social benefits and pension. In Crimea they refused to follow the disbanding order and declared they now on subordinated to the local authorities (thus forming the core of the Crimea's own forces).
It should be noted also that the new government made a strong emphasis on that the Yanukovich, the police and army officers are guilty in suppressing the revolt. Some people threatened the military personnel that they were fixing all their actions so to prosecute them later. Given such charges, the new government is no longer in moral position to order a suppression of another revolt.
That said, the actions of Russia in this situation more look as a stab in the back. Suppose you are a soldier in the trench. And you are attacked from the back of your lines rather than from the enemy's positions. First you will think it is a joke, then you will think it is a mistake, then you will try to negotiate and finally you will be totally demoralized between the lines of enemy in the front and former supposed ally in the back.
Putin already made use of situations when the West pressed Russia's friendly governments, like those in Belarus and Kyrgyzstan the most hard, to gain certain concessions for Russia. The stronger the West presses on those countries, the more does Russia demand also. This way for example, Russia gained control of much of the Belarus's industry.