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I thought your sources said they had *few artillery pieces* of inferior quality, not muskets.
Artillery pieces were few and had scarce range, while, in origin, arquebuses were just few and poorly handled, but they become progressively worse (in the sense of "not of the same level of the ones produced in the west") during the 16th century (see later).
A cannon is a big, hard thing, and often it survives a battle pretty unscathed (if does not crack). Good cannon captured were usually re-used, but bad ones (and according to letters, most of captured ottoman ones were so) and were usually melted when captured, to recuperate the metal. But after a battle, captured arquebused they were usually in pretty bad conditions (in the hurly-burly of combat there are many unhortodox ways a long piece of wood and metal could be used), and since there was no sense in melting them down (there's no much metal to recuperate), they were usually thrown away.
The problem for artillery was meanly in the weapons itself, while hand gunnery problems relied more in the scarce training of the handlers to produce a fire concentration.
But in the eye of the Vizier reading the bad report, it is not so easy to make the distintion between the quality of the weapon and the handling of it. The net results is that, seeing how much more effective was european musketry, most ottomans thought "this franks [westerns] must have exceptional arquibuses, since they are able to cause such an effect".
Thus, anybody rich or important enough pushed to be equipped with items coming from the west. As you could imagine, this did not help to increase the quality of home-made hand guns.
With the time, things worsened, since metallurgy improved faster in the west than in the empire, and hand guns become also worse per se respect to the european ones (less reliable, less range, slower to recharge).
The empire attempte to patch thing buying foreign weapon, but the solution was not effective, since trade was not enough to equip more than a few privileged units.
A second reason (most probably, the root problem) for than not being effective is the fact proper training (i.e. training aimed at maximizing fire concentration, speed up reloading, coordinate with pikemen or their equivalents) was not implemented
In definitive, the ottoman army was lacking both artillery and in small arms but the small-arm problem was perceived as the most problematic.
As I told, the point of a battle for most of the fighters was taking spoils, and for this reason even naval battles (which today we summarize as "sink the other ship", thus "use the big gun") were actually decided by musketry of the boarding/boarded troops, thus the importance of not having good handguns/not being able to handle them properly (the distinction was probably difficult to make in the head of the soldiers themselves) was considered more crucial than the artillery problem.
\And as to why these sources do not exist, I can offer a simple example of how that might be. The Axis-Soviet War, a decisive victory for the Soviet Union, written by the losers was turned into Germans overwhelmed by a faceless horde without too many details of what the Soviets did. Asking why people would never attribute anything superior to the enemy in wartime propaganda is a strange question, particularly in the 1400s and 1500s.
If you think that Pasha and Viziers (of which we have letters deploring the scarce quality of both cannons and hand guns), had in fact been suborned by enemies to spread propaganda, then I must conclude that the western spies were much more active then I have thought.
Especially since the same spies must also have altered the Topkapi registers which show the costant buying of european weapons by the empire, and the difference in equipment between elite units (few, overpaid, partly equipped with european weapons) and second-rate units (many, cheaper, equipped with items from the empire).
I do not exclude that some of those complaints could have other reasons as well (an attempt to sink a rival in the Divan, a pasha unable to accept the fact that the battle was lost because he was a poor general, even simply the writer being in a bad mood), but there is no doubt that the problem existed.