There is a military solution in Ukraine. What Kerry means--and doesn't say (an instance of not saying what you mean and therefore not being able to mean what you say)--is that the West has no military solution available that they're willing to pursue. That's a rather different sort of proposition.
Because the military solution is the simple one for Russia, and it's one that they're actively pursuing. In the absence of military hardware, an offensive, shelling of population centers and infrastructure, boots on the ground, there's be no problem in Ukraine that we'd even think "military solution" about.
There are solutions. One is to find a way to bargain for not too humiliating a defeat and not too many concessions when you're in a position of weakness. The other is to train Ukrainians and provide them with sufficient defensive weapons to deny the other side a viable military solution. It's one that Russia has actively managed to avoid by denying responsibility, keeping everything economic and political. Because while militaristic nationalism is a cheap and easy ploy, if truckloads of bodies started returning home they'd have not a Groznyi and Chechnya on their hands but an Afghanistan and a return of the "zinc boys" meme.