But now Russia has lost influence among Ukrainians...because the most influential Russians in Ukraine were in Crimea.
Ukraine needed to split. You can’t have two peoples at each other’s throats living under the same roof.
No, it's a good political move, and here is why.
If your friends and your foes are mixed together, you cannot apply any pressure onto that country without hurting both. Your influence among your friends takes damage. At the same time you cannot reward your friends without also rewarding your opponents.
What you do is you separate them. Your friends then can be managed as your friends, and your enemies can be managed as your enemies - with completely different sets of tools. Take the price on gas, for example - Crimea will get it for a song, while the rest of Ukraine will be paying what Putin tells them to pay.
Or take those NATO bases in Ukraine. Do you think Putin will allow them? The rest of Ukraine will fall to him if the politicians in Kiev just twitch in that direction. H*ll, what did the USA do when Soviet nukes showed up in Cuba? Do not expect anything less from this scenario either.
I do not believe that Putin actually needs Ukrainian land. What he needs is a neutral, stable country. The $hit hit the fan only when Ukraine experienced a political upheaval of dangerous proportions. You will tolerate your neighbor if he is just a little weird; however nobody would sit idle if the said neighbor attempts to set fire to his house - it's a stone throw from yours. This problem with Ukraine is far more fundamental than a mere desire of Putin to return Crimea.