After the Napoleons defeat there occurred several congresses and treaties defining the new Europe and trying to create a long-lasting peace, one of the main goals was an Equilibrium between the great European powers. Into consideration were taken: Prussia, Austria, France, Great Britain and Russia, however the diplomats and heads of this idea did not seem to consider the Ottoman Empire as one of those big powers, despite them controlling quite a big amount of Land within the European continent. Why was that? Did they lack military strength? was it due to the different Religions? Were they not Interested?
There are a few reasons for this. First is the fact that there were already signs that the Ottomans might be disintegrating. Because of that, they did not feel they were strong enough to be admitted into the Congress.
However, more than that, there is a notion that the Ottomans were not European. They were the perpetual foreigners at the table, as we can see from many, many sources including everything from books to coffee labels.
Religion plays a large part on this, but there is also a long history of invasion and repelling as well as the collective memory of the Crusades. The Habsburgs, for instance, had repelled the Ottoman Turks (with quite a bit of help from the Poles, I might add) in 1683, resulting in a loss of much of Hungary for the Turks.
Lastly, and perhaps most importantly, is that the Ottomans, even by this point, were seen as a Russian issue. The Russians were supposed to see what happened with the Ottomans and oversee their eventual collapse or lead defense against them in the event of their invasion. To invite them to the Congress would have been seen as an insult to the Russians and, indeed, everyone else, as it would put them as an equal to the other Empires.
If you are more interested in this, please look at sources regarding the so-called Eastern Question, relating to the "sick man of Europe." Though a bit dated, a good overview of this can be found in the book below (a great book if you are interested in the history of East Central Europe).
Source
Halecki, Oscar. Borderlands of Western Civilization: A History of East Central Europe. Ed., Andrew L. Simon. Safety Harbor, FL: Simon Publications, 1980.