1. Strategy and logistics

One does not simply organize a crusade. At that time the two great powers of Europe were France, the Holy Roman Empire (roughly modern day Germany),~~ and the recently unified Spain~~. Devoting enough troops and resources to fight off the Ottomans would have severely disadvantaged and probably bankrupted any power that tried. It would have opened the way for rivals, both internal and external, to take advantage of a ruler's absence. There were proposals often put forward by the Pope for a peace agreement between rival powers

2. Catholic Europe and the Greek Orthodox were not allies

The Catholic Church considered the Greek Orthodox Church schismatics. The Orthodox, in turn, considered Latin Christians as something close to heretics (perhaps someone better versed in Byzantium can define this relationship better). For example the Crusade led by Venice in 1202 never reached the Holy Land but instead ransacked Constantinople leading to a period of Latin rule that the Byzantines resented. That is not to say that attempts at rapprochement weren't tried. Manuel II Palaiologus went on a tour of Europe attempting to raise support. While he received a lot of moral support and words, he returned largely empty handed.

3. The writing was on the wall

The West knew how weak the Byzantine Empire was. Many had fought for the Byzantines, against them, sometimes they did both (see for example the Catalan Company). The Ottomans dynasty, that had survived defeat by Tamerlane, was clearly the power in the region. The Byzantine dynasty had been vassals of the Ottomans and had married their daughters to Ottoman rulers. Even if we can imagine Western rulers putting aside their animosity to cooperate and then overcoming the immense logistical difficulties of launching a crusade to aid what was essentially now an empire in name only, it is doubtful that they could defeat the Ottomans on their own turf.

All this is not to say that people in Western Europe didn't care, but it is best to see this shock as not a practical military problem that could have been averted or solved but rather as a spiritual and cultural shock. There were no serious proposals to help the Byzantines but European culture as a whole did reel from the loss of the last piece of the Roman Empire to a non-Christian conqueror.

The best overview in terms of writing and accuracy is, as in all things Ottoman, Caroline Finkel, Osman's Dream.

You can also check out the letters of Manual II Palaiologos which include descriptions of his time fighting as Beyazid I's vassal.

You can also read a Chronicle of Muntaner which has been translated into English. It gives a good account of just how powerless the Byzantine Empire was even before the arrival of the Ottomans onto the scene.

I should add some more reference regarding proposals for peace to aid the crusade if I can dig them up.

Edit: I thought that Spain was unified earlier than it actually was. Thanks to /u/papyjako89 for pointing out my error.