(Repost of a previous post I had done about the Fall of Constantinople and the sacking of Sophia)

The Christian world barely even noticed that Constantinople as a power existed. By the time of the fall of Constantinople, the "Empire" extended hardly more than a few miles past the city gates. It was not a world power; it wasn't even a regional power. Half the city had died 100 years before in from the Black Plague and it never quite recovered from that.

The final nail in the coffin was the fact that Catholic and Eastern Orthodox had been feuding for so long the enmity between the two couldn't be overcome. Byzantine Emperor Constantine XI wrote to Pope Nicholas V and even promised some concessions if the West would help repel the invaders. Nicholas tried to send help, but was stymied by Lords and Kings wary of the Pope gaining more control. The force that was sent wasn't enough. The city fell to the Ottomans after a 40 day siege. It was looted for 3 days by the soldiers, including the Hagia Sophia, which was promptly turned into a mosque. Interestingly enough, the Greek Orthodox Church was left alone and gained a new Patriarch. The Pope was understandably upset that not enough of Christendom came to the aid of Constantinople (especially since they agreed to the Union with the Catholic church, making him more powerful) and he forcefully called for a Crusade, and was ignored. He tried to build one for himself to lead, but died too soon to get a movement started.

Sources: http://www.ellopos.net/elpenor/vasilief/constantine-xi-capture-of-constantinople.asp http://militaryhistory.about.com/od/battleswars14011600/p/Byzantine-Ottoman-Wars-Fall-Of-Constantinople.htm# The Destruction of the Greek Empire, Edwin Pears http://coursesa.matrix.msu.edu/~fisher/hst373/readings/nicol.html http://www.greece.org/romiosini/fall.html

Looking at the time after the fall of Constantinople, it did come to be seen as a blow to Christendom - especially with Sultan Mehmed transferring the Ottoman capital there, and with subsequent rise of Ottoman intervention in the Mediterranean from the early 16th c. onwards. Papal appeals to a crusade were responded to on the Iberian peninsula were the reconquista was rekindled by the Catholic Monarchs, Ferdinand and Isabella of Aragon and Castile. This crusading spirit can be seen in a 1486 visit by both monarchs to Santiago de Compostela, praying for divine help from Santiago 'Matamoros' ('moor killer'), but can also be traced back to skirmishes between Arab and northern Spanish Visigothic troops (under semi-mythical ruler Pelayo) in the Early Middle Ages. The conquest of Granada in 1491 was directly linked by contemporaries to the fall of Constantinople, as the end of Muslim rule in Iberia was again seen as an important step in the crusade against Christianity's enemies.
Further ahead, with increasing Castilian dominance, the rivalry between Castile and the Ottoman Empire in the Mediterranean accelerated. Other European powers started becoming more involved as well, finally resulting in the Holy League's (made up of Spanish, Italian and papal forces) influential victory at Lepanto in 1571. So, while the initial reaction to the attack on Constantinople and to a call for crusade was lacking, Spanish and Italian resistance to Ottoman ascendancy intensified afterwards, with the fall of Constantinople possibly serving as a sort of 'awakening call' in Europe.
David Abulafia's 'The Great Sea' does a pretty good job of describing the rivalries at that time, with a Mediterranean focus. Specifically for Castile/Spain, see Leon P. Harvey's 'Islamic Spain 1250-1500' and/or 'Muslims in Spain 1500-1614'.

Also important is that Byzantium was not fully independent prior to its fall. Observers at the time would have watched Byzantium grow gradually more dependent on the Ottomans over the past hundred years, and so the fall was not that surprising -- it had been foretold for decades. In 1363 Murat I took the Maritsa valley, which contained the farmland that supplied Constantinople with most of its food. In response the Byzantines had to "accept some kind of subordination to the Ottomans and [sign] a treaty with Murat (1363) confirming all the Ottoman conquests in Europe and promising to refrain from plots... in return for Murat's assurance that he would not attack Constantinople and would provide it with needed food." (pg. 18, Empire of the Gazis: The Rise and Decline of the Ottoman Empire 1280-1808, Stanford J. Shaw) So in 1363 the Ottomans essentially could do whatever they liked with Byzantium. Over the next decades there would be periods, particularly the Interregnum, over which Byzantium would exert more independence, but not for the hundred years preceding its conquest was it ever truly independent.