This may be a blessing in disguise for the Ottoman Empire. It is still approaching its zenith of power, and this setback could force the Ottoman's to take some creative, corrective actions. For instance, in 1570 the Ottoman's tried to build a canal between the Don and Volga Rivers, in order to attack the Safavid capital at Tabriz through the Caspian Sea, rather than through the arid mountains to Tabriz's west (these mountains had claimed several Ottoman attempts to take the capital). With the Safavids now taking a bigger chunk of Anatolia, the Ottomans decide that a strategic outflanking of the Safavids is in order, and build the canal several decades early. The Don-Volga Canal is built with Russian slave labor, and after the building of the canal the slaves are settled around the canal. With the canal built, a successful pincer attack is executed against the Safavids, with Ottoman troops attacking Safavid possessions in Anatolia, and taking Tabriz, at the same time. The Safavid Empire is crushed. Much more of Persia is integrated into the Ottoman Empire, since the canal allows for much better power projection into Persia. It also allows for much better power projection into the old Turkish homeland in Transoxania (sp?). The importance of the Canal in taking Persia, and further conquests, means that the Ottomans make sure to take direct control of the Don and Volga Rivers, and Astrakhan. Direct control means more settlement.
In building the canal, and then in finding settlers, and then in the eternal search for the most un-populated by Turkishness janissary recruits they can find, the Ottoman move into the Don and Volga brings about some serious changes for the Grand Duchy of Russia. Vasili III, the Grand Duke at the time, spends most of his time battling the resurgent Crimean Tartars, who, now backed by the Ottoman Empire, claim the old rights of the Golden Horde over Muscovy.