Wonderful skreczok provided the answer for Russian Orthodoxy, I shall provide the same for the pope.
The army that took Byzantium in 1453 did not stop, but set on the way through Serbia to the Kingdom of Hungary. Serbia fell prior to the Ottoman Empire, but Hungary remained standing and had a full "wall" of fortifications on its southern border. One of the biggest of these fortifications, Belgrade, was on the Danube, right where the Ottomans aimed to breach into the country. Obviousy, the Ottoman army waited to recover then set off in early 1456 to capture Belgrade.
The pope knew this, all of this. And the pope was prepared. The fall of Byzantium signalled the fall of one bastion of Christianity in the east, which meant another was required.
In 1456, an actual crusade was called. In fact, the pope ordered all bells to ring at noon in Europe as a reminder of this one crusade, led by John of Capistrano, a Franciscaner monk. In the end, the pope's reaction was successful, since the Hungarian army combined with the crusader reinforcements (who were mostly peasants providing a diversion. The Hungarian cavalry swarmed in as the poor sods were slaughtered) managed to break the siege and defeat the Ottoman army.
The bells still ring at noon in every Catholic / Protestant church, as a reminder of this one victory. I find that extremely fascinating.
An interesting note here that the Hungarian victory here gave way to some local nationalism in Wallachia as well, where an old acquaintance of the Hungarian leader rose to power, Vlad the Impaler.
Here's some more reading on the Pope's side. But remember, the pope wasn't idle. The man knew that one bastion fell and had to reinforce another, and did all he could, considering the turmoil elsewhere in Catholic Europe (100 years war that just ended).
https://www.jstor.org/stable/23659810?seq=1#page_scan_tab_contents (You may need scholarly access for the full paper)
Dear Austro-Hungarian, I’ll try and give some context to the catholic reaction to the fall of Byzantium by discussing the relations between the empire and the pope in the run-up to the capture of the city as well.
The fall of Constantinople in 1453 sent shockwaves throughout Christian Europe. Even though the Byzantine Empire had been not much more than a city state for the last 50 years, and was completely surrounded by the much larger Ottoman Empire, the fall of the city came as somewhat of a surprise. (Map of the situation in 1450) The Queen of Cities had never really recovered from the brutal sack by crusaders in 1204 and was at this time a city in decay. According Steve Runciman in The Fall of Constantinople 1453, it had been reduced to a collection of villages within the walls, some separated by large swathes of agricultural land and neighbourhoods that had long been deserted.
In the run-up to the siege, Emperor Constantine XI asked the pope for aid because the Ottoman pressure was rising. The Holy See had its price for giving aid. In long and painstaking conversations between Byzantine Orthodox and Roman Catholic clerics, a union between both churches was discussed under leadership of the pope. This had been attempted multiple times in the years before the fall of the Byzantine Empire, often under strenuous demands from the Catholic side and always ending in failure. Despite this bad track record, a new union under the pope was proclaimed in 1452, grudgingly accepted by the Emperor in the hope of receiving military support for his imperiled city.
Some troops and galleys were sent to assist Constantinople from the Catholic countries. But even though these soldiers did the best they could to keep the city in Christian hands, the Byzantines knew it wasn’t nearly enough. The defenders were still hopelessly outnumbered and outgunned by the attacking Turks. The Byzantine historian Sphrantzes, who was present during the siege of Constantinople, is indignant over the lack of help from other Christians. ‘No aid whatsoever was dispatched by other Christians’ he tells his readers, before rhetorically asking his reader ‘what measures were taken by the (Catholic) Church to prevent our downfall?’ a few paragraphs later. The city fell on the 29th of May, 1453.
Despite the dire state the Byzantine Empire had been in for quite some time, this bad news was seen as a great and unexpected blow to the Christian faith. Something had to be done! According to Runciman, the then-ruling pope Nicholas V issued a bull on the 30th of September in 1453 urging Christian rulers to crusade to save Constantinople. They were called on to shed their blood and the blood of their subjects and provide a tithe of their revenue for the cause.
In the end though, there was little reaction to pope Nicholas’s call for Holy War. Most Christian princes didn’t really care for Byzantium or were occupied with their own troubles. Despite the pope’s words of saving Constantinople for Christendom, the Byzantines (generally speaking) weren’t very popular in the West, and were loathed as corrupt, decadent and effeminate. Not a lot of people were prepared to risk their lives for them, especially seeing how most previous crusades to relieve Turkish pressure on the Greeks had ended in failure.
In the 15 years after the fall of Constantinople, the remaining pockets of Byzantine successor states were absorbed by the Ottoman Empire. While there was concerted Catholic effort in fighting the Turks in Serbia, John Hunyadi’s death in 1456 quickly squished the already faint hope that Christian armies would retake Constantinople. No serious effort to do so was attempted until (arguably) the Battle of Gallipoli in the First World war.
George Sphrantzes was a Byzantine diplomat and historian. He was in the city at the time of its fall, where he was captured and later freed. Afterwards, he served the remnants of the imperial family and later became a monk and wrote his Chronicle. Excerpt here: http://militaryrevolution.s3.amazonaws.com/Primary%20sources/Sphrantzes.pdf
I can recommend Steve Runciman’s The Fall of Constantinople 1453 to anyone who wants to know more about the fall of the city. It is an accessible but thorough book, which details the run-up to and aftermath of the siege from Byzantine, Catholic and Turkish perspectives. Even though it is a little old, it is well sourced and also contains a handy overview the most important Byzantine, Catholic and Turkish sources of the period in its appendix.
